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​:

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

For this problem:

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

Inserting the result with ​x​ = 0:

The solution, b = −7, is correct.