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.