Question

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.

Answer 1

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

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
`x` ;

∴,

The number of miles '
`y`' left to walk will be :
`y=21-x`

Thus the time '
`t`' for which he walked :

`t=(distance)/(speed) \\t=(x)/(3)`:

∴

From these equations , we get :

`x=21-y\\x=3t\\21-y=3t\\y=21-3t`

Thus , when we compare this with
`y=mx+c` ,

`y=mx+c\\y=-3t+21\\m=-3,c=21`

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