Keisha makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below shows her pay (in dollars) versus the number of hours worked.
Use the graph to answer the questions.
Pay ()
y20406080100120140160180200x1234567890
Number of
hours worked
(a) What is Keisha's pay for a house call if she doesn't work any hours?
(b) What is her pay if she works 1 hour?
(c) How much does her pay increase for each hour worked?
(d) Are the amounts given in parts (b) and (c) equal?
Why or why not? Choose the best answer.
Yes, because the line passes through 0,0.
Yes, because the line does not pass through 0,0.
No, because the line passes through 0,0.
No, because the line does not pass through 0,0.
(a) Keisha's pay for a house call if she doesn't work any hours is $20.
(b) Her pay if she works 1 hour is $40.
(c) Her pay increases by $20 for each hour worked.
(d) The amounts given in parts (b) and (c) are not equal. The pay for 1 hour of work is $40, while the increase in pay for each hour worked is $20.
(a) Keisha's pay for a house call if she doesn't work any hours is $20 (y-coordinate when x = 0).
(b) Her pay if she works 1 hour is $40 (y-coordinate when x = 1).
(c) Her pay increases by $20 for each hour worked (difference in y-coordinates for consecutive x-values).
(d) The amounts given in parts (b) and (c) are not equal. The line on the graph does not pass through the point (0,0), therefore the pay is not directly proportional to the number of hours worked.
To answer these questions, we need to examine the graph provided.
(a) To find Keisha's pay for a house call if she doesn't work any hours, we look at the y-axis where the number of hours worked is 0. We can see that the corresponding point on the graph is the y-intercept, which is the point where the line crosses the y-axis. From the graph, we can see that the y-coordinate at the y-intercept is $40.
Therefore, Keisha's pay for a house call if she doesn't work any hours is $40.
(b) To find her pay if she works 1 hour, we locate the point on the graph where the number of hours worked is 1 and look at the corresponding y-coordinate. From the graph, it appears to be between $40 and $60, so we can estimate it as $50.
Therefore, her pay if she works 1 hour is $50.
(c) To determine how much her pay increases for each hour worked, we can calculate the slope of the line. The slope represents the rate at which her pay increases per hour worked. From the graph, we can visually estimate the slope by looking at the steepness of the line. Based on the scale of the y-axis, it appears that her pay increases by $20 for each hour worked.
Therefore, her pay increases by $20 for each hour worked.
(d) Now we need to determine if the amounts given in parts (b) and (c) are equal. From the graph, we can see that the line passes through the point (1, 50) and intersects the y-axis at (0, 40). Since the line passes through the origin (0, 0), we can conclude that the amounts given in parts (b) and (c) are equal.
Hence, the best answer is: Yes, because the line passes through 0,0.