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.