Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

Two point form calculator

google play badge app store badge

This online calculator finds and plots the equation of a straight line passing through the two given points. The calculator generates a step-by-step explanation of how to get the result.

Line through two points calculator
Find the line equation in both general and slop y-intercept form.
help ↓↓ examples ↓↓ tutorial ↓↓
line through two given points
General form (default)
Slope y-intercept form
Hide steps
Find approximate solution
thumb_up 1.8K thumb_down

Get Widget Code

working...
Examples
ex 1:
Determine the equation of a line passing through the points $(-2, 5)$ and $(4, -2)$.
ex 2:
Find the slope - intercept form of a straight line passing through the points $\left( \frac{7}{2}, 4 \right)$ and $\left(\frac{1}{2}, 1 \right)$.
ex 3:
If points $\left( 3, -5 \right)$ and $\left(-5, -1\right)$ are lying on a straight line, determine the slope-intercept form of the line.
Find more worked-out examples in our database of solved problems..

How to find equation of the line determined by two points?

To find equation of the line passing through points $A(x_A, y_A)$ and $B(x_B, y_B)$ ( $ x_A \ne x_B $ ), we use formula:

$$ {\color{blue}{ y - y_A = \frac{y_B - y_A}{x_B-x_A}(x-x_A) }} $$

Example:

Find the equation of the line determined by $A(-2, 4)$ and $B(3, -2)$.

Solution:

In this example we have: $ x_A = -2,~~ y_A = 4,~~ x_B = 3,~~ y_B = -2$. So we have:

$$ \begin{aligned} y - y_A & = \frac{y_B - y_A}{x_B-x_A}(x-x_A) \\ y - 4 & = \frac{-2 - 4}{3 - (-2)}(x - (-2)) \\ y - 4 & = \frac{-6}{5}(x + 2) \end{aligned} $$
two point form

Multiply both sides with $5$ to get rid of the fractions.

$$ \begin{aligned} (y - 4)\cdot {\color{red}{ 5 }} & = \frac{-6}{5}\cdot {\color{red}{ 5 }}(x + 2)\\ 5y - 20 & = -6(x + 2)\\ 5y - 20 & = -6x - 12 \\ 5y & = -6x - 12 + 20 \\ 5y & = -6x + 8 \\ {\color{blue}{ y }} & {\color{blue}{ = -\frac{6}{5}x - \frac{8}{5} }} \end{aligned} $$

In special case (when $x_A = x_B$ the equation of the line is:

$$ {\color{blue}{ x = x_A }} $$

Example 2:

two point form 2

Find the equation of the line determined by $A(2, 4)$ and $B(2, -1)$.

Solution:

In this example we have: $ x_A = 2,~~ y_A = 4,$ $ x_B = 2,~~ y_B = -1$. Since $x_A = x_B$, the equation of the line is:

$$ {\color{blue}{ x = 2 }} $$

You can see from picture on the right that in special case the line is parallel to y - axis.

Note: use above calculator to check the results.

Search our database with more than 300 calculators
362 861 664 solved problems
×
ans:
syntax error
C
DEL
ANS
±
(
)
÷
×
7
8
9
4
5
6
+
1
2
3
=
0
.