# How to Find B in Y=Mx + B

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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.

(6x - 3y) ÷ 3 = (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

6x -3y = 21

6(0) - 3(-7) = 21

0 + 21 = 21

The solution, b = -7, is correct.