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: Identify the y - intercept (base pay)

The y - intercept of a linear equation \(y = mx + b\) (where \(y\) is total pay and \(x\) is overtime hours) represents the base pay. When \(x = 0\) (no overtime hours), from the graph, \(y=\$1200\). So the base pay \(b = 1200\).

Step2: Calculate the slope (overtime rate)

The slope \(m\) of a line is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line. For example, when \(x_1 = 0,y_1=1200\) and when \(x_2 = 4,y_2 = 1400\). Then \(m=\frac{1400 - 1200}{4-0}=\frac{200}{4}=50\).

Answer:

Justin will earn his usual base pay of \(\$1200\) plus an extra \(\$50\) per hour for any overtime work.