The formula *y* = *mx* + *b* is an algebra classic. It represents a linear equation, the graph of which, as the name suggests, is a straight line on the *x*-, *y*-coordinate system.

Often, however, an equation that can ultimately be represented in this form appears in disguise. As it happens, any equation that can appear as:

where *A*, *B* and *C* are constants, *x* is the independent variable and *y* is the dependent variable is a linear equation. Note that *B* here is not the same as *b* above.

The reason for recasting it in the form

is for ease of graphing. *m* is the slope, or tilt, of the line on the graph, whereas *b* is the *y*-intercept, or the point (0. *y*) at which the the line crosses the *y*, or vertical, axis.

If you already have an equation in this form, finding *b* is trivial. For example, in:

All terms are in the proper place and form, because *y* has a *coefficient* of 1. The slope *b* in this instance is simply −7. But sometimes, a few steps are required to get there. Say you have an equation:

To find *b*:

## Step 1: Divide All Terms in the Equation by B

This reduces the coefficient of *y* to 1, as desired.

## Step 2: Rearrange the Terms

For this problem:

The *y*-intercept, *b* is therefore **−7**.

## Step 3: Check the Solution in the Original Equation

Inserting the result with *x* = 0:

The solution, b = −7, is correct.