A participant in a 21-mile walkathon walks at a steady rate of 3 miles per hour. He thinks, The relationship between the number of miles left to walk and the number of hours I already walked can be represented by a line with slope -3.” Do you agree with his claim? Explain your reasoning.
I agree with the claim that the relationship between the number of miles left to walk and the number of hours already walked can be represented by a line with a slope of -3.
We know that the participant walks at a steady rate of 3 miles per hour. So, for every hour he walks, he covers a distance of 3 miles. Therefore, if we consider the number of hours already walked as the x-axis and the number of miles left to walk as the y-axis, the relationship between the two variables can be represented by the equation: y = -3x + b, where b is a constant.
The slope of a line is the change in y divided by the change in x. In this case, the change in y (number of miles left to walk) is -3 times the change in x (number of hours already walked). This verifies that the slope of the line is indeed -3, as the participant suggested.
Therefore, I agree with the claim that the relationship between the number of miles left to walk and the number of hours already walked can be represented by a line with slope -3.