Video Tutorial
on Finding the Equation of a line From 2 points
Slope intercept vs Point Slope Form
There are a few different ways to find the equation of line from 2 points.
The first half of this page will focus on writing the equation in slope intercept form like example 1 below.
However, if you are comfortable using the point slope form of a line, then skip to the second part of this page because writing the equation from 2 points is easier with point slope form .
Example
Equation from 2 points using Slope Intercept Form
Find the equation of a line through the points (3,7) and (5,11)
Step 1Calculate the slope from 2 points
Substitute the slope for 'm' in the slope intercept form of the equation
y = mx +b
y = 2x +b
Substitute either point into the equation. You can use either (3,7) or (5,11)
Solve for b, which is the y-intercept of the line
Substitute b, -1, into the equation from step 2
Use our Calculator
You can use the calculator below to find the equation of a line from any two points. Just type numbers into the boxes below and the calculator (which has its own page here) will automatically calculate the equation of line in point slope and slope intercept forms
Answer:
$ $
( Try this 'equation from 2 points' calculator on its own page here . )
Practice Problems
Calculate the slope from 2 points
Substitute the slope for 'm' in the slope intercept form of the equation
y = mx +b
y = ½x +b
Substitute either point into the equation. You can use either (4,5) or (8,7)
Solve for b, which is the y-intercept of the line
Substitute b, 3, into the equation from step 2
Calculate the slope
Substitute the slope for 'm' in the slope intercept equation
Substitute either point into the equation. You can use either (-6,7) or (-9,8)
Solve for b, which is the y-intercept of the line
Substitute b, 5, into the equation from step 2
$$ y = \frac{1}{3}x +\red{b} \\ y = \frac{1}{3}x +\red{5} $$
Calculate the slope
Substitute the slope for 'm' in the slope intercept equation
Substitute either point into the equation. You can use either (-3,6) or (15,-6)
Substitute b, -1, into the equation from step 2
Example 2
Equation from 2 points using Point Slope Form
As explained at the top, point slope form is the easier way to go. Instead of 5 steps, you can find the line's equation in 3 steps, 2 of which are very easy and require nothing more than substitution! In fact, the only calculation, that you're going to make is for the slope.
The main advantage, in this case, is that you do not have to solve for 'b' like you do with slope intercept from.
Find the equation of a line through the points (3,7) and (5,11)
Step 1Calculate the slope from the 2 points
Step 2
Substitute the slope for 'm' in the point slope equation
y − y1 = m(x −x1)
y − y1 = 2(x −x1)
Substitute either point as x1, y1 in the equation. You can use either (3,7) or (5,11)
using (3,7):
y − 7 = 2(x− 3)
using (5,11):
y − 11 = 2(x − 5)
Practice Problems
Calculate the slope from 2 points
Substitute the slope for 'm' in the point slope equation
y − y1 = m(x −x1)
y − y1 = ½(x −x1)
Substitute either point into the equation. You can use either (4,5) or (8,7)
using (4,5):
y − 5 = ½(x − 4)
using (5,11) :
y − 11 = ½(x − 5)
Calculate the slope from 2 points
Substitute the slope for 'm' in the point slope equation
y − y1 = m(x −x1)
y − y1 = 
(x −x1)
Substitute either point into the equation. You can use either (-6,7) or (-9,8)
using (-6,7):
y − 7 = (x + 6)
using (-9, 8):
y − 8 = (x +9)
Calculate the slope from 2 points
Substitute the slope for 'm' in the point slope equation
y − y1 = m(x −x1)
y − y1 = 
(x −x1)
Substitute either point into the equation -3,6) and (15,-6)
using (-3, 6):
y − 6 = (x + 3)
using (15, -6):
y + 6 = (x − 15 )
If you read this whole page and looked at both methods (slope intercept form and point slope, you can see that it's substantially quicker to find the equation of line through 2 points by means of point slope
