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Bot GPT 4-o mini 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**.