# How to Find Slope From an Equation

••• jacoblund/iStock/GettyImages
Print

A linear equation is one that relates the first power of two variables, x and y, and its graph is always a straight line. The standard form of such an equation is

Ax + By + C = 0

where A, B and C are constants.

Every straight line has slope, usually designated by the letter m. Slope is defined as the change in y divided by the change in x between any two points (x1, y1) and (x2, y2) on the line.

m = ∆y/∆x = (y2 - y1) ÷ (x2 - x1)

If the line passes through point (a, b) and any other random point (x, y), slope can be expressed as:

m = (y - b) ÷ (x - a)

This can be simplified to produce the slope-point form of the line:

y - b = m(x - a)

The y-intercept of the line is the value of y when x = 0. The point (a, b) becomes (0, b). Substituting this into the slope-point form of the equation, you get the slope-intercept form:

y = mx + b

You now have all you need to find the slope of a line with a given equation.

## General Approach: Convert from Standard to Slope-Intercept Form

If you have an equation in standard form, it takes just a few simple steps to convert it to slope intercept form. Once you have that, you can read slope directly from the equation:

1. ## Write the Equation in Standard Form

2. Ax + By + C = 0

3. ## Rearrange to Get y by Itself

4. By = -Ax - C

y = -(A/B)x - (C/B)

5. ## Read Slope from the Equation

6. The equation y = -A/B x - C/B has the form y = mx +b, where

m = -(A/B)

## Examples

Example 1: What is the slope of the line 2x + 3y + 10 = 0?

In this example, A = 2 and B = 3, so the slope is -(A/B) = -2/3.

Example 2: What is the slope of the line x = 3/7y -22?

You can convert this equation to standard form, but if you're looking for a more direct method to find slope, you can also convert directly to slope intercept form. All you have to do is isolate y on one side of the equal sign.

1. ## Add 22 to Both Sides and Put the y Term on the Right

2. 3/7y = x + 22

3. ## Multiply Both Sides by 7

4. 3y = 7x + 154

5. ## Divide Both Sides by 3

6. y = (7/3)x + 51.33

This equation has the form y = mx + b, and

m = 7/3