Question

Clive and Erica both have part-time jobs where they get paid by the hour. Erica makes more than Clive. The number of dollars, dd, Clive makes in hh hours can be modeled by the equation d=9.5hd=9.5h.

Erica created a graph, with the number of hours she works along the xx-axis and the number of dollars she makes along the yy-axis. Her graph is a line with a slope of 99 and a yy-intercept is 00. Which is a true statement?

Answer 1

Missing Options:

A. Erica's graph is incorrect, because the slope should be greater than 9.5.

B. Erica's graph is incorrect, because the y-intercept should be greater than 9.5.

C. Erica's graph is correct, because the slope should be less than 9.5.

D. Erica's graph is correct, because the y–intercept should be less than 9.5.

Answer:

A. Erica's graph is incorrect, because the slope should be greater than 9.5.

Explanation:

Given

Clive:

`d = 9.5h`

Erica:

`m = 9` --- slope

`b =0` --- y intercept

First, we need to determine the equation of Erica's earnings using

`d = mh + b`

Where

m = slope = 9

b = y intercept = 0

So, the equation becomes

`d = 9 * h + 0`

`d = 9h + 0`

`d = 9h`

This implies that Erica earns 9 dollars per hour

For Clive:

`d = 9.5h`

This means that Clive earns 9.5 dollars per hour

From the question, we understand that Erica earns more than Clive.

So, we can conclude that Erica's graph is incorrect because the slope must be greater than 9.5.

When the slope is greater than 9.5, then she earns more than Clive.