A participant in a 21-mile walkathon walks at a steady rate of 3 per hours. 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.

Yes. I agree with his claim because the equation relating the miles left to walk and the number of miles left to walk is : [tex]y=-3t+21[/tex]

Step-by-step explanation:

Given :

It's a 21 - mile walkathon
The rate at which he is moving is 3 miles per hour.

Let the number of miles walked be [tex]x[/tex] ;

∴,

The number of miles '[tex]y[/tex]' left to walk will be : [tex]y=21-x[/tex]

Thus the time '[tex]t[/tex]' for which he walked :

[tex]t=\frac{distance}{speed} \\t=\frac{x}{3}[/tex]:

∴

From these equations , we get :

[tex]x=21-y\\x=3t\\21-y=3t\\y=21-3t[/tex]

Thus , when we compare this with [tex]y=mx+c[/tex] ,

[tex]y=mx+c\\y=-3t+21\\m=-3,c=21[/tex]

Thus this is an equation of a Line with slope -3.