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.