Question

Write the equation for this situation, then give the x-intercept, y-intercept, and slope. A person is wanting to burn 500 calories a day through excercise. They know that they burn 7.3 calories a minute jogging and 11.3 calories a minute running. ALSO - explain what the x and y-intercepts mean in this situation. Your answer:

Answer 1

`x`-intercept is
`(68.5,0)`

`y`-intercept is
`(0,44.2)`

Explanation:

Let
`x` denotes time denoted (in minutes) by a person in jogging.

Let
`y` denotes time denoted (in minutes) by a person in running.

A person is wanting to burn 500 calories a day through exercise. They know that they burn 7.3 calories a minute jogging and 11.3 calories a minute running.

So, equation becomes
`7.3x+11.3y=500`

For
`x`-intercept, put
`y=0`

`7.3x+11.3(0)=500\\7.3x=500\\x=68.5`

So,
`x`-intercept is
`(68.5,0)`

For
`y`-intercept, put
`x=0`

`7.3(0)+11.3y=500\\11.3y=500\\y=44.2`

So,
`y`-intercept is
`(0,44.2)`

Differentiate equation
`7.3x+11.3y=500` with respect to
`x`

`7.3+11.3y'=0\\y'=(-7.3)/(11.3)\\ y'=-0.65`

`x-`intercept means that a person spends 68.5 minutes in jogging and no time in running.

`y-`intercept means that a person spends 44.2 minutes in running and no time in jogging.