Question

A waiter earns an hourly wage plus tips made during a shift. The graph shows the total earnings based on the number of hours worked.Which equation represents the total amount the waiter earns, y, based on the number of hours worked, x?

Answer 1

To determine the waiter's earnings, y, based on the number of hours worked, x, you have to determine the y-intercept and slope of the line.

The y-intercept is the point where the line crosses the y-axis, in this example it indicates the waiter's earning when he worked x=0 hours. The y-intercept is (0,35)

To determine the slope of the line you need to use the following formula

`m=(y_1-y_2)/(x_1-x_2)`

Where

m is the slope

(x₁,y₁) are the coordinates of one point of the line

(x₂,y₂) are the coordinates of a second point of the line

Using the points (4,45) and (2,40) you can determine the slope of the line as follows:

`\begin{gathered} m=(45-40)/(4-2) \\ m=(5)/(2)\approx2.5 \end{gathered}`

The slope of the line is m=2.5, this means that the waiter's earnings increase by 2.5 for each hour worked.

Using the slope-intercept form you can determine the equation as follows:

`y=mx+b`

Where

m is the slope

b is the y-coordinate of the y-intercept

For m=2.5 and b=35, the equation that corresponds to the total earnings of the waiter based on the hours worked is