What Is Two Point Form in Math?
Two point form in math is one of the important methods to find the equation of a line when coordinates of any two points on the line are known. The equation of a line is used to represent each and every point on the line, we can say that it is satisfied by each point on the line.
Let

The two-point form is given by
Two Point Form: Definition
If
OR
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Two Point Form Formula
The two points formula of two point form of an equation is given as-
Let
Here,
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Derivation of Two Point Form Formula
Let
Let

From the figure, we can observe that the three points
Slope of line MP
Or
Equation of a Line in Two-Point Form
The equation of a line in the two-point form is given by
or
where
How To Write Equation of a Line in Two Point Form
Let’s understand the steps to find the equation of a line using two-point form.
- Name the coordinates of the given two points as
and . - Substitute the values in the Two-Point formula given by
- Simplify.
Finding Equation of a Line Using Two Point Form
To write equation of a line in two-point form, simply substitute the coordinates of the given two points in the equation
Example: Find the equation of a line passing through the points
Here,
Substitute the values in
Deriving Two Point Form Using Point Slope Form
Let

The two-point slope form of the straight line passing through these points is given by “m”:
The Point-Slope form equation of a line is given by:
Substituting 1 in 2:
Facts about Two Point Form!
- The two-point form of a line can also be written as given:
Or
- An exceptional case where the two-point form cannot be used is the equation of a vertical line passing through point (a, b) given by
. Slope of the vertical line is not defined.
Conclusion
In this article, we learned about two-point forms of a line. Let us now look at some examples and practice some problems to understand the concept better.
Solved Examples On Two Point Form
1. Find the equation of the line passing through the points:
Solution:
The given points are:
The equation of a straight line passing through the points
Substituting the values, we get:
Therefore, this is the required equation of a line passing through the given points.
2. What is the equation of a straight line passing through the points (3, 0) and (0, 3)?
Solution:
Let’s write the coordinates as
The equation of a straight line passing through the points
Substituting the values, we get
Therefore, the equation of a line passing through the given points
3. Find the equation of a line with two points
Solution:
Given : Two points on the straight line are
The equation of a straight line passing through the points
Substitute
4. Find the equation of a straight line whose x-intercept is “a” and y-intercept is “b.”
Solution: The line passes through the points
Substituting the values
Dividing both sides by ab, we get:
Thus, the equation of the given line is given as:
This is also known as the intercept-form of a line.
5. Derive the y-intercept of the line with the coordinates given by:
Solution:
Let the given points be:
The equation of a straight line passing through the points
Now, multiplying both sides by
The line equation from two points is given above.
The final equation of the slope-intercept form is written as-
Comparing our equation to the standard form, we will get y-intercept, b as
Further, the slope of the line (m) can be given as
Practice Problems On Two Point Form
Two Point Form – Definition, Derivation, Formula, Examples
What is the equation of the line in the slope point form?
The equation of a straight line passing through the points
What is the equation of a straight line passing through the points (5, 0) and (0, 5)?
Substitute
Substituting the values, we get;
Therefore, the equation of a line passing through the given points
What is the slope of a line passing through the points and .
The slope of a straight line passing through the points
Slope
Substitute
Slope
What is the equation of a vertical line passing through the point ?
The equation of a vertical line passing through the point
The equation of a vertical line passing through the point
Frequently Asked Questions On Two Point Form
How do you determine whether a point lies on a line?
Every point on a line satisfies its line equation. For example, to see whether (3, 6) lies on a line
What is the point slope form?
The equation of line in point slope form is given by
What is the equation of x-axis?
The equation of x-axis is
What is the equation of y-axis?
The equation of y-axis is x = 0.