Question

Graphing Linear Equations Unit Test
8 of 188 of 18 Items












Question
Use the image to answer the question.

An illustration shows two graphs depicting earnings per hour for employees 1 and 2. The first graph shows earnings per hour for employee 1. The horizontal axis shows hours ranging from 0 to 8 in increments of 2. The vertical axis shows earnings in dollars ranging from 0 to 80 in increments of 5. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 4 comma 50 right parenthesis, and left parenthesis 6 comma 75 right parenthesis. A line connects all the data points. The second graph shows earnings per hour for employee 2. The horizontal axis shows hours ranging from 0 to 6 in increments of 1. The vertical axis shows earnings in dollars ranging from 0 to 80 in increments of 5. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 15 right parenthesis, left parenthesis 3 comma 45 right parenthesis, and left parenthesis 5 comma 75 right parenthesis. A line connects all the data points.

The earnings for Employee 1 and Employee 2 are displayed in the following graphs. Which employee earns more per hour?

(1 point)
Employee
earns more per hour.

Answer 1

To determine which employee earns more per hour, we need to find the slope of the lines representing the earnings for both employees, as the slope indicates the rate of change or the earnings per hour.

For Employee 1, we can use the points provided:
- Point 1: (0, 0)
- Point 2: (2, 25)
- Point 3: (4, 50)
- Point 4: (6, 75)

To find the earnings per hour (slope), we can take two points and use the slope formula:
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using points (0, 0) and (2, 25):
\[
\text{slope} = \frac{25 - 0}{2 - 0} = \frac{25}{2} = 12.5 \text{ dollars per hour}
\]

For Employee 2, we can also use the points provided:
- Point 1: (0, 0)
- Point 2: (1, 15)
- Point 3: (3, 45)
- Point 4: (5, 75)

Using points (0, 0) and (1, 15):
\[
\text{slope} = \frac{15 - 0}{1 - 0} = 15 \text{ dollars per hour}
\]

Comparing the slopes (earnings per hour):
- Employee 1: $12.5 per hour
- Employee 2: $15 per hour

Thus, Employee 2 earns more per hour.

Final answer: **Employee 2 earns more per hour.**