https://file.aiquickdraw.com/mathbot/file/1726797588737zqnmujut.jpg

From the image, you are given a table of statements about two cars, Car A and Car B, and you need to determine whether each statement is true or false based on a graph that shows the speed of the two cars over time.

### The statements to assess:
1. **The line for Car A has a constant of proportionality of 70.**
2. **Car B is traveling faster than Car A.**
3. **The line for Car B has a constant of proportionality of 90.**
4. **The constant of proportionality of the line for Car A is greater than that for Car B.**
5. **It takes longer for Car B to travel the same distance as Car A.**

### Graph Interpretation:
- From the graph, the distance (y-axis) increases with time (x-axis) for both cars. The slope of the line for each car represents its speed, which is constant since both cars have straight lines. The steeper the slope, the faster the car is traveling.
- The speed of Car A appears to be 70 miles per hour (from the slope of the line labeled as Car A), and the speed of Car B is 90 miles per hour (from the slope of the line labeled as Car B).

### Evaluating Each Statement:
1. **True**: The slope for Car A is 70 miles per hour, so its constant of proportionality is indeed 70.
2. **False**: Car B is traveling faster than Car A, as its slope is steeper, meaning Car B has a greater speed (90 mph) compared to Car A (70 mph).
3. **True**: The slope for Car B is 90 miles per hour, so the constant of proportionality for Car B is 90.
4. **False**: The constant of proportionality for Car A (70) is less than that for Car B (90), so the statement is false.
5. **False**: Since Car B is traveling faster than Car A, Car B will take less time to travel the same distance.

### Final Table:

| Statement                                                                                         | True | False |
|---------------------------------------------------------------------------------------------------|------|-------|
| The line for car A has a constant of proportionality of 70.                                        |   X  |       |
| Car B is traveling faster than car A.                                                             |      |   X   |
| The line for car B has a constant of proportionality of 90.                                        |   X  |       |
| The constant of proportionality of the line for car A is greater than the constant of car B.       |      |   X   |
| It takes longer for car B to travel the same distance as car A.                                   |      |   X   |

Let me know if you need further clarification on any of these answers!

### Related Questions:
1. How do you calculate the slope from a distance-time graph?
2. What is the relationship between speed and slope in a distance-time graph?
3. Can a car have a non-constant speed on a distance-time graph? How would that look?
4. How do you determine which car is faster based on a distance-time graph?
5. What would it mean if the two cars had lines that were parallel in this graph?

**Tip**: A steeper slope on a distance-time graph indicates a faster speed, as more distance is covered in less time.

The graph shows the average speed of two cars, Car A and Car B. You are asked to determine whether each statement in the table is true or false based on the graph.

Analyze a distance-time graph to determine the speed of two cars and assess statements about their proportionality. Learn key concepts such as speed calculation, linear equations, and constant rate of change. Suitable for students in Grades 6-8.

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