Question

justin is a nurse at westwood general hospital. this week, he will earn his usual base pay as well as an additional amount for each hour he works overtime. this situation can be modeled as a linear relationship. complete the statement that describes the situation. justin will earn his usual base pay of plus an extra per hour for any overtime work.

Explanation:

Step1: Find the base pay

The base pay is the \(y\) - intercept of the linear relationship. When the number of overtime hours (\(x\)) is \(0\), the total pay (\(y\)) is \(1200\). So the base pay is \(\$1200\).

Step2: Calculate the slope (extra pay per hour)

Use the formula for the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,1200)\) and \((x_2,y_2)=(5,1500)\) (we can pick any two points on the line). Then \(m=\frac{1500 - 1200}{5-0}=\frac{300}{5}=60\)

Answer:

Justin will earn his usual base pay of \(\$1200\) plus an extra \(\$60\) per hour for any overtime work.