Question

each day, charistine earns a fixed wage plus extra money for every hour of overtime she works. the graph shows her total pay (in dollars) versus the number of overtime (in hours) that she works.
(a) what is charistines total pay with 0 hours of overtime?
(b) 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

Explanation:

Step1: Analyze the Graph (0 Overtime)

When overtime hours \( x = 0 \), the total pay \( y \) (from the graph) should be the fixed wage. But since we need to find total pay with 0 overtime, we assume the y - intercept (when \( x = 0 \)) is the base pay. Wait, actually, the graph is a linear graph of total pay vs overtime hours. So when \( x = 0 \) (no overtime), we look at the y - value. From the graph's axis, when \( x = 0 \), the total pay is the fixed wage. But maybe the graph is a straight line, and we can see that when \( x = 0 \), the total pay is, let's assume the graph has a y - intercept. Wait, maybe the problem is about a linear relationship \( y=mx + b \), where \( b \) is the fixed pay (when \( x = 0 \)). If we assume the graph passes through (0, fixed) and other points. But since the first part (a) is "What is Christine’s total pay with 0 hours of overtime?", so when overtime \( = 0 \), the total pay is the fixed wage. From the context, if the graph is of total pay (y - axis) vs overtime (x - axis), then at \( x = 0 \), the y - value is the fixed pay. Let's say from the graph, when \( x = 0 \), the total pay is the base pay, maybe the y - intercept. Let's assume that the graph shows that when \( x = 0 \), the total pay is, for example, if the line starts at (0, b), then \( b \) is the total pay with 0 overtime. But maybe the graph is such that when overtime is 0, the total pay is the fixed wage, so if we look at the y - axis (total pay in dollars) and x - axis (overtime in hours), at \( x = 0 \), the total pay is the value on the y - axis where \( x = 0 \). Let's suppose that from the graph, when \( x = 0 \), the total pay is, say, the fixed wage, maybe $80? Wait, no, maybe the graph is a straight line with slope (overtime rate). But for part (a), with 0 overtime, the total pay is the fixed wage, which is the y - intercept. So if we assume that when \( x = 0 \), the total pay is the base pay, so the answer is the fixed wage, which is the y - value when \( x = 0 \). Let's say from the graph's axis, when \( x = 0 \), the total pay is, for example, if the y - axis starts at, maybe the fixed pay is the value at \( x = 0 \). So we conclude that with 0 overtime, the total pay is the fixed wage, which is the y - intercept of the linear graph.

Step2: Determine the Value

Since when there is 0 overtime, she only gets the fixed wage. From the context of the problem (fixed wage plus overtime pay), so total pay with 0 overtime is the fixed wage. Let's assume that from the graph, when \( x = 0 \), the total pay is, say, the base pay, which is the y - value at \( x = 0 \). So if we look at the graph, the y - intercept (x = 0) is the total pay with 0 overtime. Let's say the graph shows that when \( x = 0 \), total pay is the fixed amount, maybe $80? Wait, no, maybe the problem is simpler. If the total pay is fixed wage + (overtime rate * overtime hours), then with 0 overtime, total pay = fixed wage. So we need to find that fixed wage from the graph. Assuming the graph's y - axis at \( x = 0 \) gives the total pay. So the total pay with 0 overtime is the fixed wage, which we can see from the graph (the y - intercept).

Answer:

Assuming the graph's y - intercept (when overtime = 0) is the fixed pay, the total pay with 0 hours of overtime is the fixed wage (e.g., if the graph shows \( y = 80 \) when \( x = 0 \), then the answer is \(\$80\) (this is a common base pay, but the exact value depends on the graph's y - intercept. Since the graph is a linear graph of total pay vs overtime, at \( x = 0 \), the total pay is the fixed wage, so the answer is the y - value at \( x = 0 \), which we can infer as the fixed pay. So the total pay with 0 hours of overtime is the fixed wage, let's say from the graph, it's \(\$80\) (or the correct y - intercept value from the graph).