Finding the Equation of a Line Given Two Points:
Most people when asked, “What is the equation of a line?”, will answer, “y = mx + b”. This is the
equation of a line in what is called slope-intercept form where “m” is the slope and “b” is the y-
intercept. So, how do you find the equation of a line? There are several different ways that you can find
the equation of a line. I find the equation of a line everytime by following the same three steps:
Step 1: Find the slope of the line.
Step 2: Use the slope to find the y-intercept.
Step 3: Use steps 1 and 2 to write the answer.
I will explain these steps by looking a several examples. Please understand that there are often several
different ways to complete each math problem, but I have found through the years that students are most
successful when the do problems the same way each and every time they attempt the problem. If you
know a different way to find the answer that is great, but I am going to show how to do the problem one
way and use the same technique everytime I see this problem.
Example 1: Find the equation of the line passing through the points (–1, –2) and (2, 7).
Step 1: Find the slope of the line.
To find the slope of the line passing through these two points we need to use the slope
formula:
( )
( )
So the slope of the slope of the line passing through these two points is 3.
Step 2: Use the slope to find the y-intercept.
Now that we know the slope of the line is 3 we can plug the slope into the equation and
we get:
y = 3x + b
Next choose one of the two point to plug in for the values of x and y. It does not matter
which one of the two points you choose because you should get the same answer in either
case. I generally just choose the first point listed so I don’t have to worry about which
one I should choose.
(–1, –2) → –2 = 3(–1) + b Multiply to simplify the problem.
–2 = –3 + b Solve for b and you will have the y-intercept. b=1
Step 3: Write the answer.
Using the slope of 3 and the y-intercept of 1, the answer is:
y = 3x + 1