13.3Linear Equations

Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form:

$y = a + bx y=a+bx$

where a and b are constant numbers.

The variable x is the independent variable, and y is the dependent variable. Another way to think about this equation is a statement of cause and effect. The X variable is the cause and the Y variable is the hypothesized effect. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.

Example 13.1

The following examples are linear equations.

$y=3+2xy=3+2x$
$y=–0.01+1.2xy=–0.01+1.2x$

The graph of a linear equation of the form y = a + bx is a straight line. Any line that is not vertical can be described by this equation.

Example 13.2

Graph the equation y = –1 + 2x.

Figure 13.3
Try It 13.2

Is the following an example of a linear equation? Why or why not?

Figure 13.4

Example 13.3

Aaron's Word Processing Service (AWPS) does word processing. The rate for services is $32 per hour plus a$31.50 one-time charge. The total cost to a customer depends on the number of hours it takes to complete the job.

Find the equation that expresses the total cost in terms of the number of hours required to complete the job.

Solution 13.3

Let x = the number of hours it takes to get the job done.
Let y = the total cost to the customer.