To determine the unit rate of the faster horse, we need to examine the speed (distance per unit time) for both horses, Horse A and Horse B.

Step 1: Calculate the Unit Rate for Horse A

From the graph:

• At $x = 1$ minute, $y = 500$ meters.
• This gives a unit rate (or speed) for Horse A of: $\text{Speed of Horse A} = \frac{\text{distance}}{\text{time}} = \frac{500 \text{ meters}}{1 \text{ minute}} = 500 \text{ meters per minute}$

Step 2: Determine the Unit Rate for Horse B

For Horse B, the distance $y$ in meters can be represented by the equation: $y = 530x$ This equation indicates that Horse B runs 530 meters in 1 minute. Therefore: $\text{Speed of Horse B} = 530 \text{ meters per minute}$

Step 3: Compare the Unit Rates

Horse B has a unit rate of 530 meters per minute, while Horse A has a unit rate of 500 meters per minute. Since 530 meters per minute is faster, Horse B is the faster horse.

Conclusion

The correct answer is:

• 530 meters per minute

Would you like further details or have any questions?

Here are some related questions to deepen understanding:

1. How would the unit rate change if Horse B's equation were $y = 550x$?
2. What is the significance of the slope in Horse B's equation $y = 530x$?
3. If Horse A continued at this speed for 10 minutes, how far would it travel?
4. How would you represent Horse A's movement with an equation?
5. What other methods can we use to determine which horse is faster?

Tip: The unit rate in a linear equation like $y = kx$ is represented by the constant $k$, which is the slope of the line.