1.2 Forms of Linear Functions

There are two forms of linear functions you should know: slope-intercept form and general form. The most familiar way to write a linear function is slope-intercept form:

$y=mx+b$

In this form, m is the slope that describes the linear relationship between x and y, and b is the y-intercept, which provides the value of y (output variable) when x (input variable) is equal to 0.

In a previous math class, you may also have seen a linear equation in the general formaxbyc, or standard form:

$ax+by=c$

Let’s run through an example to help you gain the intuition behind this form. Suppose you want to hire some full-time and part-time employees. The cost of full-time employment is $70,000 per year, and the cost of part-time employment is $15,000 per year on average. Assume that $x$ represents the number of full-time employees and $y$ the number of part-time employees. The equation that represents this situation is

$70,000x+15,000y=c$

where $c$ is the total annual cost of wages to pay to your employees. If you have one full-time employee and four part-time employees, the annual cost is

$70,000\times 1+15,000\times 4=130,000$