A. The amount fof money that Carl earns is $15 per hour.
B. Carl earns more per hour.
C. A graph that represents Carl's earnings over time in hours is shown below.
In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:
y = kx
Where:
- y represents the y-variable or money earned ($).
- x represents the x-variable or time (in hours).
- k is the constant of proportionality.
Part A.
Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 45/3 = 75/5 = 120/8 = 150/10
Constant of proportionality, k = 15.
Therefore, the required linear function for Carl's earnings over time is given by;
y = kx
y = 15x, which means that Carl earns $15 per hour.
Part B.
Based on the equation, y = 12x, Louis earns $12 per hour. In this context, we can logically deduce that Carl earns more per hour;
y = 12(1) = $12 per hour.
y = 15(1) = $15 per hour.
Part C.
In conclusion, we would use an online graphing tool to plot Carl's earnings over time in hours as shown in the image below.
Missing information:
The equation y= 12x describes the amount of money Louis earns, where x is the number of hours he works and y is the amount of money he earns. The table shows the amount of money Carl earns for different numbers of hours worked.
A) How much money does Carl earn per hour? Show your work.
B) Who earns more per hour? Justify your answer.
C) Draw a graph that represents Carl's earnings over time in hours. Remember to label the axes.