How to Find B in Y=Mx + B

••• joel-t/iStock/GettyImages

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:

Ax + By = C

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

y = mx + b

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:

y = -5x -7

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:

6x - 3y = 21

To find ​b​:

Step 1: Divide All Terms in the Equation by B

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

\frac{6x - 3y}{3} = \frac{21}{3} \\ \,\\ 2x - y = 7

Step 2: Rearrange the Terms

For this problem:

-y = 7 + 2x \\ y = -7 - 2x \\ y = -2x -7 \\

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

Step 3: Check the Solution in the Original Equation

Inserting the result with ​x​ = 0:

6x -3y = 21 \\ (6 × 0) - (3 × -7) = 21 \\ 0 + 21 = 21

The solution, b = −7, is correct.


About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at