Compare Proportional Relationships Practice
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.
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
.
The equation for Employee 2 is
.
The equation for Employee 1 is y = 10x, where y represents the earnings and x represents the hours worked.
The equation for Employee 2 is y = 15x, where y represents the earnings and x represents the hours worked.
the equivalent of line is y=-2x-4 what is the y-intercpt
The equation for Employee 1 is y = 10x, where x represents the number of hours worked and y represents the earnings.
The equation for Employee 2 is y = 15x, where x represents the number of hours worked and y represents the earnings.
To find the equation that represents the proportional relationship between the earnings and hours worked for each employee, we need to look at the data given.
For Employee 1, the table shows the earnings per hour as follows:
Hours | Earnings
1 | 10
2 | 20
3 | 30
To find the equation, we need to determine the constant of proportionality, which is the amount earned per hour. We can calculate this by dividing the earnings by the hours worked. Looking at the data, we can see that for each hour worked, the earnings increase by 10. So, the constant of proportionality is 10. Therefore, the equation for Employee 1 is Earnings = 10 * Hours.
For Employee 2, we have a line graph with plotted points:
(0, 0)
(1, 15)
(3, 45)
(5, 75)
To find the equation, we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept. Looking at the graph, we can see that the line passes through the origin (0, 0). This means that the y-intercept, b, is 0.
To find the slope, we can use the formula: slope (m) = change in y / change in x. Taking two points from the graph (0, 0) and (1, 15):
slope (m) = (15 - 0) / (1 - 0) = 15 / 1 = 15
Therefore, the equation for Employee 2 is Earnings = 15 * Hours.
So, the equation representing the proportional relationship between the earnings and hours worked for Employee 1 is Earnings = 10 * Hours, and for Employee 2 is Earnings = 15 * Hours.