Compare Proportional Relationships Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Use the table and image to answer the question.

This table shows the hourly earnings of Employee 1 along with the corresponding total earnings based on hours worked.
Employee 1
Earnings per Hour
Hours Earnings
1 10
2 20
3 30
A line graph is titled as Employee 2, Earnings per Hour. The x-axis is labeled Hours ranging from 0 to 6 in increments of 1. The y-axis is labeled Earnings in dollars, ranging from 0 to 80 in increments of 5. A solid line joins four plotted points. The coordinates of the plotted points are as follows: 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.

The proportional relationship for the earnings and hours worked for Employee 1 is displayed in the table. The proportional relationship between the earnings and hours worked for Employee 2 is displayed in the graph. What is the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2?

(1 point)
The equation for Employee 1 is y=

The equation for Employee 2 is y=

Answer 1

To determine the equations representing the proportional relationships between earnings and hours worked for both Employee 1 and Employee 2, we can analyze the information given.

For Employee 1:

The information in the table shows the hourly earnings:

• For 1 hour, the earnings are $10.
• For 2 hours, the earnings are $20.
• For 3 hours, the earnings are $30.

From this data, we can see that the earnings (y) are directly proportional to the hours worked (x). The relationship can be expressed with the formula: \[ y = kx \] where \( k \) represents the constant of proportionality (the earnings per hour).

In this case, since every hour worked corresponds to an earning of $10, we can deduce that: \[ k = 10 \] Thus, for Employee 1, the equation is: \[ y = 10x \]

For Employee 2:

From the graph, we see the plotted points:

• (0, 0)
• (1, 15)
• (3, 45)
• (5, 75)

To find the equation for Employee 2, we determine the constant of proportionality from the earnings for 1 hour, which is $15:

Using a similar relationship: \[ y = kx \]

Here, at 1 hour, the earning is $15, so: \[ k = 15 \] Thus, for Employee 2, the equation is: \[ y = 15x \]

Final Answers:

• The equation for Employee 1 is: y = 10x
• The equation for Employee 2 is: y = 15x