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

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 (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}) on the line.

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

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

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:

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:

## Write the Equation in Standard Form

## Rearrange to Get y by Itself

## Read Slope from the Equation

The equation

has the form

where

## Examples

**Example 1:** What is the slope of the line

In this example, *A* = 2 and *B* = 3, so the slope is

**Example 2**: What is the slope of the line

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.

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

## Multiply Both Sides by 7

## Divide Both Sides by 3

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