Questions: The graph shows the earnings for x hours for Employee 1. The table shows the earnings for x hours for Employee 2. Which employee earns more? Explain. Hours, x 1 2 3 4 Earnings, y (dollars) 18 36 54 72 Employer 2 20 per hour < 18 per hour If so, identify the constant of proportionality.

The graph shows the earnings for x hours for Employee 1. The table shows the earnings for x hours for Employee 2. Which employee earns more? Explain.

Hours, x 1 2 3 4
Earnings, y (dollars) 18 36 54 72

Employer 2
20 per hour < 18 per hour
If so, identify the constant of proportionality.

Transcript text: The graph shows the earnings for $x$ hours for Employee 1. The table shows the earnings for $x$ hours for Employee 2. Which employee earns more? Explain. \begin{tabular}{|l|c|c|c|c|} \hline Hours, $\boldsymbol{x}$ & 1 & 2 & 3 & 4 \\ \hline Earnings, $\boldsymbol{y}$ (dollars) & 18 & 36 & 54 & 72 \\ \hline \end{tabular} $\square$ Employer 2 \[ \$ 20 \text { per hour }<\$ 18 \text { per hour } \] If so. identify the constant of proportionality.

Solution

Solution Steps

Step 1: Find the earnings per hour for Employee 1.

The graph for Employee 1 passes through the point (2, 30). This means that in 2 hours, Employee 1 earns $30. So, the earnings per hour for Employee 1 is $30/2 = $15.

Step 2: Find the earnings per hour for Employee 2.

From the table, we see that Employee 2 earns $18 in 1 hour, $36 in 2 hours, $54 in 3 hours, and $72 in 4 hours. In each case, the earnings divided by the hours is $18. So, Employee 2 earns $18 per hour.

Step 3: Compare the earnings.

Employee 1 earns $15 per hour, and Employee 2 earns $18 per hour. Therefore, Employee 2 earns more.