{"id":28082,"date":"2023-04-27T09:25:43","date_gmt":"2023-04-27T09:25:43","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=28082"},"modified":"2024-10-28T10:39:39","modified_gmt":"2024-10-28T10:39:39","slug":"negative-slope-definition-graph-solved-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope","title":{"rendered":"Negative Slope: Definition, Graph, Solved Examples, Facts"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-d8e5bd45-671e-4161-92c7-1fb1fd3392d0\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope#0-what-is-a-negative-slope>What Is a Negative Slope?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope#3-how-to-calculate-negative-slope>How to Calculate Negative Slope<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope#4-types-of-slope>Types of Slope<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope#7-solved-examples-on-negative-slope>Solved Examples on Negative Slope<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope#8-practice-problems-on-negative-slope>Practice Problems on Negative Slope<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope#9-frequently-asked-questions-on-negative-slope>Frequently Asked Questions on Negative Slope<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-negative-slope\">What Is a Negative Slope?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Negative slope refers to the slope of a line that is trending downwards as we move from left to right. <\/strong>In mathematics, the slope of a line is the change in y-coordinate with respect to the change in x-coordinate.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, <strong>what does negative slope mean?<\/strong> A negative slope means that two variables are negatively related. When x increases, y decreases.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>A line that makes an obtuse angle (an angle greater than 90 degrees) with the positive x-axis in the counterclockwise direction is known as a line with a negative slope. <\/strong>If the line makes an acute angle with the positive direction of the x-axis, the line has a positive slope. A simple real-life example of negative slope is going down a hill.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-negative-slope-negative-rise-over-run-ratio\">Negative Slope: Negative Rise Over Run Ratio<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We know that the slope is given by the rise over run ratio.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope $= m = \\frac{Rise}{Run} = \\frac{\\Delta y}{\\Delta x}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can also say that a line has a negative slope when it has a negative rise over run ratio. Rise is the change in y-coordinates, and run is the change in x-coordinates. Let\u2019s take a look at example of the negative slope equation with graphs showing rise over run ratio.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1:<\/strong> Here, the line AB has a slope of $\\frac{-1}{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Equation of line is $y = \\frac{-1}{2}x + 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope $= \\frac{Rise}{Run} = \\frac{-1}{2}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"609\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/line-y-equal-to-minus-12x-plus-1-with-negative-slope.png\" alt=\"line y = -12x + 1 with negative slope\" class=\"wp-image-36998\" title=\"line y = -12x + 1 with negative slope\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/line-y-equal-to-minus-12x-plus-1-with-negative-slope.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/line-y-equal-to-minus-12x-plus-1-with-negative-slope-300x295.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2:<\/strong> Here, the line $y = \\frac{-1}{3}x + 5$ has the rise over run ratio equal to $\\frac{-1}{3}$.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"665\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Negative-Slope-2.png\" alt=\"\" class=\"wp-image-28101\" title=\"graph of a line y = -13x+5 having negative slope\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Negative-Slope-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Negative-Slope-2-280x300.png 280w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-negative-slope-graph\">Negative Slope Graph<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A line with a negative slope goes downward as we move in the positive direction of the x-axis. Mathematically, it means that as x increases, y decreases.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, what does a negative slope look like? Take a look at the blue line shown below.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">You can see that the blue line is trending downwards as it moves from left to right.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"628\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/graph-of-a-line-with-negative-slope.png\" alt=\"Graph of a line with negative slope\" class=\"wp-image-37000\" title=\"Graph of a line with negative slope\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/graph-of-a-line-with-negative-slope.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/graph-of-a-line-with-negative-slope-296x300.png 296w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-calculate-negative-slope\">How to Calculate Negative Slope<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s discuss methods to calculate negative slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Method (i)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">When the coordinates of two points on the line are given, we can use this method.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example:<\/strong> A line passes through points (4,2) and (3,5). To find if the line has a negative slope, we can use the slope formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us assume $(x_1,\\;y_1) = (4,\\;2)$ and $(x_2,\\;y_2) = (3,\\;5)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope(m) $= \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Then we have $m = \\frac{5 \\;-\\; 2}{3 \\;-\\; 4} = \\frac{3}{-\\;1} = -\\;3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since m has a negative value, the line passing through points (4,2) and (3,5) has a negative slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Method (ii)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the equation of a line is of the form $ax + by = c$, then we can use this method.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example:<\/strong> The equation of a line is $2x + 3y = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can rewrite the equation as $y = \\frac{-\\;2}{3} x + \\frac{5}{3}$<\/p>\n\n\n\n<p>If we equate the above equation with the general equation of the line in the slope-intercept form, which is $y = mx + c$ (here in the equation, m is the slope of the line, and c is the intercept made by the line with the x-axis)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Comparing the equation $y = \\frac{-\\;2}{3} x + \\frac{5}{3}$ with $y = mx + c$, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We get $m = \\frac{-2}{3}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since m has a negative value, the line $2x + 3y = 5$ has a negative slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Method (iii)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the angle made by the line with the x-axis is given, then we can use this method.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: <\/strong>If a line makes an angle of 135 degrees with the positive direction of the x-axis then to find the negative slope, we use the slope formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the line makes an angle of 135 degrees with the positive direction of the x-axis, the slope of that line will be<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$m = tan\\; 135^\\circ = tan\\; (90 + 45) = -\\;tan\\; (45)= \\;-1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the given line has a negative slope.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-types-of-slope\">Types of Slope<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are four types of slope.<\/p>\n\n\n\n<ol class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\"><strong>Positive slope<\/strong>: A line that makes an acute angle with the positive direction of the x-axis has a positive slope. The line with a positive slope rises up as we move from left to right.<br><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>Negative Slope<\/strong>: A line that makes an obtuse angle with the positive x-axis has a negative slope. The line with a negative slope sinks down as we move from left to right.<br><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>Zero slopes<\/strong>: A line that makes an angle of 0 degrees with the positive x-axis has zero slope. The line with zero slope does not have a rise, it remains horizontal, parallel to the x-axis.<br><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>Undefined slope: <\/strong>A line that makes 90 degrees with the positive x-axis has an undefined slope. The line with an undefined slope is a vertical line or a line parallel to the y-axis.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"396\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/line-with-zero-positive-negative-and-undefined-slopes.png\" alt=\"Line with zero, positive, negative, and undefined slopes.\" class=\"wp-image-37001\" title=\"Line with zero, positive, negative, and undefined slopes.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/line-with-zero-positive-negative-and-undefined-slopes.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/line-with-zero-positive-negative-and-undefined-slopes-300x192.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-facts-about-negative-slope\">Facts about Negative Slope<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\">There are four types of slopes: (i) positive slope (ii) negative slope (iii) zero slope and (iv) undefined slope<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The negative slope makes an angle greater than 90 degrees with the positive direction but makes an angle less than 90 degrees with the negative direction of the x-axis.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about the negative slope and properties of lines having a negative slope. Let\u2019s solve a few examples and practice problems based on these concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-negative-slope\">Solved Examples on Negative Slope<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Find whether the line passing through the points (5,2) and (2,-5) has a negative slope.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We have the slope formula<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;Slope$(m) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us assume $(x_1,\\;y_1) = (5,\\;2)$ and $(x_2,\\;y_2) = (2,\\;-5)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, we have to find $y_2\\;-\\;y_1 = (\\;-5)\\;-2 = \\;-7$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Again, we are to find $x_2\\;-\\;x_1 = 2\\;-\\;5 = \\;-3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now using the formula, Slope$(m) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} =\\frac{-7}{-3} = \\frac{7}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the value of the slope(m) is positive, the line passing through the points (5,2) and (2,-5) does not have a negative slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Show that the line with equation <\/strong>$5x + 2y = 5$<strong> has a negative slope.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The equation of a line is given as<strong> <\/strong>$5x + 2y = 5$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2y = -\\; 5x + 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = \\frac{-\\;5}{2} x + \\frac{5}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Rewriting the equation as $y = \\frac{-\\;5}{2}x + \\frac{5}{2}$ to compare it with the general form of a line in slope-intercept form, which is $y = m x + c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, we get the value of $m = \\frac{-5}{2}$ which is a negative number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the line <strong>\u00a0<\/strong>$5x + 2y = 5$ has a negative slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Show that the line that makes an angle of 60 degrees with the positive direction of the x-axis does not have a negative slope.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We have a formula of slope(m) $= tan\\; \\theta$; here$\\theta$ is the angle made by the line with the positive direction of the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is given that the line makes an angle of 60 degrees with the positive direction of the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, slope(m) $= \\tan\\;60^\\circ = \\sqrt{3}$, which is a positive value.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the line with an angle of 60 degrees along the positive direction of the x-axis does not have a negative slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Show that the line that makes an angle of 150 degrees with the positive direction of the x-axis has a negative slope.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>We have a formula of slope(m) $= tan\\; \\theta$; here $\\theta$ is the angle made by the line with the positive direction of the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is given in the question that the line makes an angle of 150 degrees with the positive direction of the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, slope$(m) = tan\\; 150^\\circ = tan\\;(90 + 60) =\\;-\\frac{1}{3}$, which is a negative value.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore the line with an angle of 150 degrees along the positive direction of the x-axis has a negative slope.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-negative-slope\">Practice Problems on Negative Slope<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Negative Slope: Definition, Graph, Solved Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The line that makes an angle greater than 90 degrees with the positive x-axis has  __________  slope.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">positive<\/div><div class=\"spq_answer_block\" data-value=\"1\">negative<\/div><div class=\"spq_answer_block\" data-value=\"2\">undefined<\/div><div class=\"spq_answer_block\" data-value=\"3\">zero<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: negative<br\/>The line that makes an angle greater than 90 degrees along the direction of the positive x-axis has a negative slope.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If a line makes an angle of 45 degrees with the negative direction of the x-axis then the line has ______________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">positive slope<\/div><div class=\"spq_answer_block\" data-value=\"1\">negative slope<\/div><div class=\"spq_answer_block\" data-value=\"2\">undefined slope<\/div><div class=\"spq_answer_block\" data-value=\"3\">zero slopes<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: negative slope<br\/>If a line makes an angle of 45 degrees with the negative direction of the x-axis, then that line makes an angle of $(180\\;-\\;45) = 135$ degrees with the positive direction of the x-axis, which is an obtuse angle. So, the line has a negative slope.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If a line has an equation $3x\\;-\\;3y = 1$, then the line has a _________ slope.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">zero<\/div><div class=\"spq_answer_block\" data-value=\"1\">negative<\/div><div class=\"spq_answer_block\" data-value=\"2\">undefined<\/div><div class=\"spq_answer_block\" data-value=\"3\">positive<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: positive<br\/>The equation of a line is $3x\\;-\\;3y = 1$.<br>\r\nRewrite it as $y = x \\;-\\; \\frac{1}{3}$<br>\r\nComparing it with the equation $y = mx + c$, we get $m = 1$, which means that the line has a positive slope.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If a line has an equation $3x + 3y = 8$ then this line has a ____________ slope.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">undefined<\/div><div class=\"spq_answer_block\" data-value=\"1\">zero<\/div><div class=\"spq_answer_block\" data-value=\"2\">negative<\/div><div class=\"spq_answer_block\" data-value=\"3\">positive<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: negative<br\/>The equation of a line is $3x + 3y = 8$<br>\r\nRewrite it as $y = \\;-x  + \\frac{8}{3}$<br>\r\nComparing it with the equation $y = mx + c$, we get  $m = -1$, which means that the line has a negative slope.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Negative Slope: Definition, Graph, Solved Examples, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Negative Slope\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n 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                \"text\": \"The line that makes an angle greater than 90 degrees along the direction of the positive x-axis has a negative slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"undefined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line that makes an angle greater than 90 degrees along the direction of the positive x-axis has a negative slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"zero\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line that makes an angle greater than 90 degrees along the direction of the positive x-axis has a negative slope.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"negative\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The line that makes an angle greater than 90 degrees along the direction of the positive x-axis has a negative slope.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The line that makes an angle greater than 90 degrees along the direction of the positive x-axis has a negative slope.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis then the line has ______________.\",\n                    \"text\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis then the line has ______________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis, then that line makes an angle of $$(180\\\\;-\\\\;45) = 135$$ degrees with the positive direction of the x-axis, which is an obtuse angle. So, the line has a negative slope.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"positive slope\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis, then that line makes an angle of $$(180\\\\;-\\\\;45) = 135$$ degrees with the positive direction of the x-axis, which is an obtuse angle. So, the line has a negative slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"undefined slope\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis, then that line makes an angle of $$(180\\\\;-\\\\;45) = 135$$ degrees with the positive direction of the x-axis, which is an obtuse angle. So, the line has a negative slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"zero slopes\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis, then that line makes an angle of $$(180\\\\;-\\\\;45) = 135$$ degrees with the positive direction of the x-axis, which is an obtuse angle. So, the line has a negative slope.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"negative slope\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis, then that line makes an angle of $$(180\\\\;-\\\\;45) = 135$$ degrees with the positive direction of the x-axis, which is an obtuse angle. So, the line has a negative slope.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If a line makes an angle of 45 degrees with the negative direction of the x-axis, then that line makes an angle of $$(180\\\\;-\\\\;45) = 135$$ degrees with the positive direction of the x-axis, which is an obtuse angle. So, the line has a negative slope.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If a line has an equation $$3x\\\\;-\\\\;3y = 1$$, then the line has a _________ slope.\",\n                    \"text\": \"If a line has an equation $$3x\\\\;-\\\\;3y = 1$$, then the line has a _________ slope.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The equation of a line is $$3x\\\\;-\\\\;3y = 1$$.<br>\r\nRewrite it as $$y = x \\\\;-\\\\; \\\\frac{1}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get $$m = 1$$, which means that the line has a positive slope.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"zero\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a line is $$3x\\\\;-\\\\;3y = 1$$.<br>\r\nRewrite it as $$y = x \\\\;-\\\\; \\\\frac{1}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get $$m = 1$$, which means that the line has a positive slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"negative\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a line is $$3x\\\\;-\\\\;3y = 1$$.<br>\r\nRewrite it as $$y = x \\\\;-\\\\; \\\\frac{1}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get $$m = 1$$, which means that the line has a positive slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"undefined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a line is $$3x\\\\;-\\\\;3y = 1$$.<br>\r\nRewrite it as $$y = x \\\\;-\\\\; \\\\frac{1}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get $$m = 1$$, which means that the line has a positive slope.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"positive\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The equation of a line is $$3x\\\\;-\\\\;3y = 1$$.<br>\r\nRewrite it as $$y = x \\\\;-\\\\; \\\\frac{1}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get $$m = 1$$, which means that the line has a positive slope.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The equation of a line is $$3x\\\\;-\\\\;3y = 1$$.<br>\r\nRewrite it as $$y = x \\\\;-\\\\; \\\\frac{1}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get $$m = 1$$, which means that the line has a positive slope.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If a line has an equation $$3x + 3y = 8$$ then this line has a ____________ slope.\",\n                    \"text\": \"If a line has an equation $$3x + 3y = 8$$ then this line has a ____________ slope.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The equation of a line is $$3x + 3y = 8$$<br>\r\nRewrite it as $$y = \\\\;-x  + \\\\frac{8}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get  $$m = -1$$, which means that the line has a negative slope.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"undefined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a line is $$3x + 3y = 8$$<br>\r\nRewrite it as $$y = \\\\;-x  + \\\\frac{8}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get  $$m = -1$$, which means that the line has a negative slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"zero\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a line is $$3x + 3y = 8$$<br>\r\nRewrite it as $$y = \\\\;-x  + \\\\frac{8}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get  $$m = -1$$, which means that the line has a negative slope.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"positive\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a line is $$3x + 3y = 8$$<br>\r\nRewrite it as $$y = \\\\;-x  + \\\\frac{8}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get  $$m = -1$$, which means that the line has a negative slope.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"negative\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The equation of a line is $$3x + 3y = 8$$<br>\r\nRewrite it as $$y = \\\\;-x  + \\\\frac{8}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get  $$m = -1$$, which means that the line has a negative slope.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The equation of a line is $$3x + 3y = 8$$<br>\r\nRewrite it as $$y = \\\\;-x  + \\\\frac{8}{3}$$<br>\r\nComparing it with the equation $$y = mx + c$$, we get  $$m = -1$$, which means that the line has a negative slope.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-negative-slope\">Frequently Asked Questions on Negative Slope<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\"><strong>How to find the slope using rise over run?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\">\n\n<p class=\"eplus-wrapper\">Rise over run is just a non-technical term for defining slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope $= \\frac{Rise}{Run} = \\frac{\\Delta y}{\\Delta x} = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\"><strong>What is the rise and run slope?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\">\n\n<p class=\"eplus-wrapper\">The slope of a line that is expressed in a fraction is referred to as rise over run. The numerator is the rise, which describes the change in y and the denominator of that fraction is run, which describes the change in x.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\"><strong>How do you know if a slope is negative or positive using the graph?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\">\n\n<p class=\"eplus-wrapper\">If the graph of a line rises from left to right, the slope is positive. Here, as x increases, y increases.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the graph of the line falls from left to right the slope is negative. Here, as x increases, y decreases. Here, as x increases, y decreases.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\"><strong>Does a line with a negative slope look like a horizontal line or vertical line?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\">\n\n<p class=\"eplus-wrapper\">A line with a negative slope does not look like a horizontal or vertical line. A negative slope line goes downward as we move along the x-axis.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\"><strong>Can the slope be negative?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-3c5a4338-059f-4bd2-85a1-4542aa73b3c7\">\n\n<p class=\"eplus-wrapper\">Yes, the slope of a line is negative when the line falls as we move from left to right. Here, the rise over run ratio is negative.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Negative Slope? Negative slope refers to the slope of a line that is trending downwards as we move from left to right. In mathematics, the slope of a line is the change in y-coordinate with respect to the change in x-coordinate.&nbsp;&nbsp; So, what does negative slope mean? A negative slope means that &#8230; <a title=\"Negative Slope: Definition, Graph, Solved Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope\" aria-label=\"More on Negative Slope: Definition, Graph, Solved Examples, Facts\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-28082","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28082","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=28082"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28082\/revisions"}],"predecessor-version":[{"id":42201,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28082\/revisions\/42201"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=28082"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=28082"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=28082"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}