# 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

**) needed for our equations:**

*b*## 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

**. You can also graph the equation and check to see if both points are on the line.**

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