the distance y in miles that train A travels in x hours is represented by the equation y=64x. The distance that train B travels is represented by a graph of a line through the points(0,0) and (1,60). Wich train is faster

To determine which train is faster, we need to compare the speeds of the two trains. The speed of a train can be determined by the slope of the line representing the distance traveled over time.

### Train A:
The equation representing the distance \( y \) in miles that train A travels in \( x \) hours is given by:
\[ y = 64x \]

This equation is of the form \( y = mx \), where \( m \) is the speed of the train in miles per hour. For train A:
\[ m = 64 \text{ miles per hour} \]

### Train B:
The distance that train B travels is represented by a graph of a line through the points \((0,0)\) and \((1,60)\). To find the speed of train B, we need to calculate the slope of the line passing through these points.

The slope \( m \) of a line through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \((0,0)\) and \((1,60)\):
\[ m = \frac{60 - 0}{1 - 0} = \frac{60}{1} = 60 \text{ miles per hour} \]

### Comparison:
- Train A travels at 64 miles per hour.
- Train B travels at 60 miles per hour.

**Conclusion:**
Train A is faster than Train B.

Would you like any further details or have any questions?

### Related Questions:

1. How do you find the slope of a line given two points?
2. If train A traveled for 3 hours, how far would it go?
3. If train B traveled for 3 hours, how far would it go?
4. What would the equation be for train B's travel distance?
5. How would the graph for train A look?
6. How would you graph train B's travel distance?
7. What is the importance of the slope in understanding speed?
8. How can you compare the speeds of two trains using their distance-time equations?

### Tip:
When comparing speeds using distance-time graphs, the steeper the slope of the line, the faster the speed. The slope represents the rate of change of distance with respect to time.

Learn how to compare the speeds of two trains using their distance-time equations. Train A travels at 64 miles per hour, and Train B travels at 60 miles per hour. Understand the concepts of linear equations and the slope of a line with practical examples. Suitable for students in Grades 7-9.

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