The graph below shows the weekly salaries of two employees based on the number of items sold.

Question

Salaries

A graph has items sold on the x-axis and weekly salary on the y-axis. A line for Dreya goes through points (0, 500) and (4, 600). A line for Marsha goes through points (0, 250) and (3, 400).

Which statement best explains who earns the most money per item sold?
Dreya earns the most money per item sold because her line increases at a faster rate than Marsha’s.
Marsha earns the most money per item sold because her line increases at a faster rate than Dreya’s.
Dreya earns the most money per item sold because her line begins at a higher point than Marsha’s.
Marsha earns the most money per item sold because her line begins at a higher point than Dreya’s.

Answer 1

To determine who earns the most money per item sold, we need to look at the slopes of the lines representing each employee's salary based on items sold.

First, we can calculate the slope (rate of increase of salary per item sold) for each person:

1. Dreya:

   • Points: (0, 500) and (4, 600)
   • Slope = (Change in salary) / (Change in items sold) = (600 - 500) / (4 - 0) = 100 / 4 = 25.
   • Thus, Dreya earns $25 per item sold.

2. Marsha:

   • Points: (0, 250) and (3, 400)
   • Slope = (Change in salary) / (Change in items sold) = (400 - 250) / (3 - 0) = 150 / 3 = 50.
   • Thus, Marsha earns $50 per item sold.

Now we can compare the two slopes:

• Dreya earns $25 per item sold.
• Marsha earns $50 per item sold.

Since $50 (Marsha) > $25 (Dreya), this means Marsha earns more per item sold.

The correct statement is: Marsha earns the most money per item sold because her line increases at a faster rate than Dreya’s.