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

Answer:

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

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

Step-by-step 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 $x$

$7.3+11.3y'=0\\y'=\frac{-7.3}{11.3}\\ y'=-0.65$

$x-$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.