Question

the graph represents a mechanics labor costs for a given number of hours of car repair.

car repairs

labor costs ($)

labor time (hours)

which statement describes the relationship between labor cost and time for a car repair?

all repairs requiring 1 hour or less have the same labor cost.

there is no cost of labor for a repair requiring less than 1 hour.

labor costs for a repair are less expensive as the number of hours increases.

labor costs the same no matter how many hours are used for a repair.

Explanation:

1. Analyze the first option: The graph shows that for \( x \leq 1 \) (labor time ≤ 1 hour), the labor cost \( y = 50 \) (constant). So repairs taking 1 hour or less have the same labor cost.
2. Analyze the second option: For \( x < 1 \) (e.g., \( x = 0.5 \)), \( y = 50 \), so there is a labor cost. Thus, this statement is false.
3. Analyze the third option: For \( x > 1 \), as \( x \) (hours) increases, \( y \) (cost) increases (the line has a positive slope). So labor costs become more expensive as hours increase, making this statement false.
4. Analyze the fourth option: For \( x > 1 \), cost increases with hours, so cost is not the same for all hours. This statement is false.

Answer:

A. All repairs requiring 1 hour or less have the same labor cost.