How to Find a Linear Equation Using Two Points

By Daphne Sakavellas

Edited by Eman Hamed


Let's say you are given two points: (2, -4) and (3,6) and you need to find the equation of the line they cross through in y=mx+b form, also called slope-intercept form.


(2, -4) & (3, 6)


First, you must find the slope, which is a number that describes both the direction and the steepness of a line.


To do this, you set one of the order pairs as (X1, Y1) and the other as (X2, Y2):


(2, -4) = (X1, Y1)

(3, 6) = (X2, Y2)


Then, plug the values you set into the following equation, which solves for the slope (m), or the change in y/the change in x:









In this example, we would plug in the following:


m = 6-(-4)/3-2


This can be reduced further through simplification.


m = 6+4/1

m = 10/1

m = 10


That means the m of our y=mx+b (A.K.A. the slope) equation is 10. We have y=10x+b so far.


Next, we simply plug in one of the ordered pairs to our equation and solve until b is the last remaining variable.


Point selected: (3, 6)

y = 10x+b

6 = 10(3)+b

6 = 30+b


We then solve for b by rearranging the equation:


6 = 30+b

-24 = b

b = -24


Finally, we have both variables (m and b) needed for our equations:


y = 10x-24


Plug in either of the two points into the equation to check your solution, by plugging in the x-coordinate for x and the y-coordinate for y. You can also graph the equation and check to see if both points are on the line.


Thus, our final equation in this example is y=10x-24.

38 views0 comments

Related Posts

See All