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Find Equation of Line From 2 Points

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.
Slope Intercept Form The first half of this page will focus on writing the equation in slope intercept form like example 1 below.
Point Slope Form
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 1: Equation from 2 points using Slope Intercept Form

Find the equation of a line through the points (3 ,7) and (5,11)
Step 1) Calculate the slope from 2 points step 1 find slope
Step 2) Substitute the slope for 'm' in the slope intercept form of the equation y = mx +b
y = 2x +b
Step 3) Substitute either point into the equation. You can use either (3 ,7) or (5,11) Step 3
Step 4) Solve for b, which is the y-intercept of the line Step 4 the y intercept
Step 5) Substitute b, -1, into the equation from step 2 Final Equation of Line
Practice Problems
Problem 1) Find the equation of a line through the following 2 points:
(4 , 5) and (8,7)

Step 1
Problem 2) Find the equation of a line through the following the points :
(-6 , 7) and (-9, 8)

Step 1
Problem 3) Find the equation of a line through the following the 2 points :
(-3 , 6) and (15, -6)

Step 1

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 1) Calculate the slope from the 2 points step 1 find slope
Step 2) Substitute the slope for 'm' in the point slope equation y − y1 = m(x −x1)
y − y1 = 2(x −x1)
Step 3) 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
Problem 1) Find the equation of a line through the following 2 points:
(4 , 5) and (8,7)

Step 1
Problem 2)
If a line goes through the following 2 points, what is the line's equation? (-6 , 7) and (-9, 8)

Step 1
Problem 3) Find the equation of a line through the following the 2 points :
(-3 , 6) and (15, -6)

Step 1
If you read this whole page and looked at both methods (lope intercept fro 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.