Let's analyze the problem step by step.

Problem Details:

1. The participant is walking a 21-mile walkathon at a steady rate of 3 miles per hour.
2. He proposes the relationship between the miles left to walk and the hours walked can be represented as a line with a slope of -3.

Key Understanding:

• The number of miles left to walk decreases as time increases.
• At $t = 0$ (the start), the total distance left to walk is $21$ miles.
• After $t$ hours, the miles left to walk decreases by $3t$.

The equation for this relationship can be written as: $\text{Miles left to walk} = 21 - 3t$

This is a linear equation of the form $y = mx + b$, where:

• $m = -3$ is the slope (rate of change of miles left to walk with respect to time).
• $b = 21$ is the y-intercept (initial distance at time $t = 0$).

Answer to the Question:

The participant is correct. The relationship is a linear equation with a slope of $-3$, representing the steady decrease in the miles left to walk as time increases.

Would you like more details or further explanation? Let me know!

Related Questions:

1. What would the equation look like if the walking rate changed to 4 miles per hour?
2. How long will it take for the participant to complete the walkathon?
3. Can you graph the relationship between time and miles left to walk?
4. How would the slope change if the walkathon started at 30 miles instead of 21?
5. If the participant took a break for an hour, how would the equation change?

Tip:

To identify the slope of a line in a real-world context, consider the rate of change between the dependent and independent variables. Here, the slope $-3$ reflects the steady decrease in miles walked per hour.