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

Answer:

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

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 $x$ ;

∴,

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

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

$t=\frac{distance}{speed} \\t=\frac{x}{3}$:

∴

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.