Ruthie needs to get her car fixed at a car repair shop. The relationship between time in hours it will take for a car repair and the labor charges in dollars is shown on the graph below.

Question

The graph is titled 'Car Repair' and shows time in hours on the horizontal x-axis from 0 to 4 in increments of 1, and labor charges in dollars on the vertical y-axis from 0 to 400 in increments of 100. A straight line starts at the point (0, 50) and passes through the points (2, 200) and (4, 350).

What are the slope and the y-intercept of the function? What do the slope and the y-intercept mean in relation to Ruthie’s car repair?

A.
The slope of the function is 50, which means that the labor charge is $50 for each hour it takes to repair Ruthie's car. The y-intercept is 75, which means that there is a one-time fee of $75, which could be the amount for a part needed to repair Ruthie’s car or a fee charged to look at the car to determine what repairs are needed.

B.
The slope of the function is 75, which means that the labor takes 75 hours to repair Ruthie's car. The y-intercept is 50, which means that the garage will charge $50 for each hour it takes to repair Ruthie’s car.

C.
The slope of the function is 50, which means that the labor takes 50 hours to repair Ruthie's car. The y-intercept is 75, which means that the garage will charge $75 for each hour it takes to repair Ruthie's car.

D.
The slope of the function is 75, which means that the labor charge is $75 for each hour it takes to repair Ruthie's car. The y-intercept is 50, which means that there is a one-time fee of $50, which could be the amount for a part needed to repair Ruthie’s car or a fee charged to look at the car to determine what repairs are needed.

Answer 1

To determine the slope and the y-intercept from the information provided, we can analyze the given points on the graph.

1. Identifying Key Points:
   • The y-intercept is where the line crosses the y-axis (where x = 0). According to the information given, this point is (0, 50). Therefore, the y-intercept is 50.
   • The slope (m) can be calculated by using two points on the line, such as (0, 50) and (2, 200). The slope formula is: \[ m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \]
   • Here, (x1, y1) = (0, 50) and (x2, y2) = (2, 200).
   • This gives us: \[ m = \frac{(200 - 50)}{(2 - 0)} = \frac{150}{2} = 75 \]

Thus, the slope is 75, meaning that for each hour it takes to repair the car, the labor charge increases by $75.

2. Interpretation of Slope and Y-Intercept:
   • The slope (75) indicates that the labor charge is $75 for each hour that it takes to repair Ruthie's car.
   • The y-intercept (50) indicates that there is a one-time fee of $50, which could be a charge for looking at the car or a diagnostic fee.

Now, let's review the options provided based on our findings:

• A: Incorrect because the slope is not 50 and the y-intercept is not 75.
• B: Incorrect because the slope is not 75 hours and the y-intercept is not 50.
• C: Incorrect because the slope is not 50 hours and the y-intercept is not 75.
• D: Correct because the slope is 75 (charge per hour) and the y-intercept is 50 (one-time fee).

Therefore, the correct answer is D.