Question

each day, lucy earns a fixed wage plus extra money for every hour of overtime she works. the graph shows her total pay (in dollars) versus the amount of overtime (in hours) that she works. (a) choose the statement that best describes how the amount of overtime and total pay are related. then fill in the blank. as the amount of overtime increases, the total pay decreases. at what rate is the total pay decreasing? $ per hour as the amount of overtime increases, the total pay increases. at what rate is the total pay increasing? $ per hour (b) what is lucys total pay with 0 hours of overtime? $

Explanation:

Step1: Analyze the graph trend

The graph is a line with a positive slope (going up from left to right), so as overtime (x) increases, total pay (y) increases.

Step2: Find the rate of increase (slope)

The y - intercept (when x = 0) is 75 (fixed wage). Let's take two points. When x = 0, y = 75; when x = 5, let's see the y - value. From the graph, when x = 5, y = 75+5r (r is rate). But looking at the grid, when x = 5, y seems to be 75 + 5*10=125? Wait, let's calculate slope. Slope m=\(\frac{y_2 - y_1}{x_2 - x_1}\). Take (0,75) and (5,125) (assuming, since from 0 to 5 hours, pay goes from 75 to 125? Wait, the graph: at x = 0, y = 75; at x = 5, y = 125? Wait, the y - axis: 75, 90, 105, 120, 135. Wait, when x = 0, y = 75. When x = 1, y = 90? Wait, 90 - 75 = 15? Wait, maybe my initial point was wrong. Wait, the graph: the y - intercept is at (0,75). Then, let's take another point. Let's say when x = 1, y = 90 (since 75 + 15 = 90). Then slope (rate) is \(\frac{90 - 75}{1 - 0}=\frac{15}{1}=15\). Wait, but let's check again. Wait, the y - axis: 75, 90, 105, 120, 135. So each hour, the pay increases by 15. So the rate of increase is 15 per hour.

Step3: Part (b)

When overtime (x) is 0, the total pay is the y - intercept, which is 75 dollars (from the graph, when x = 0, y = 75).

Part (a)

• The correct statement is "As the amount of overtime increases, the total pay increases."
• The rate of increase is 15 dollars per hour (calculated as slope, \(\frac{\Delta y}{\Delta x}=\frac{90 - 75}{1 - 0}=15\) or any other two points, e.g., (2,105): \(\frac{105 - 75}{2 - 0}=\frac{30}{2}=15\)).

Part (b)

When x = 0 (0 hours of overtime), the total pay is 75 dollars (from the y - intercept of the graph).

Answer:

s:
(a) Statement: As the amount of overtime increases, the total pay increases. Rate: \(\$15\) per hour.
(b) \(\$75\)