Question

3. The grade a student earns on a test varies directly with the amount of time the student spends studying. Suppose a student spends 5.5 hours studying and makes a grade of 76% on the test. What is an equation that relates the grade earned on a test, g, with the amount of time spent studying, t, in hours? What is the garish of your equation.

Answer 1

The required equation is
`g=13.8182t`.

Explanation:

Consider the provided information.

It is given that The grade a student earns on a test varies directly with the amount of time the student spends studying.

First find the slope of the line using the formula:
`m=(Rise)/(Run)`

Since the grade rise to 76 after spending 5.5 hours studying.

Thus, the slope of the line is:
`m=(76)/(5.5)=13.8182`

It is given that equation varies directly with the amount of time the student spends studying.

Thus the equation should be in form of
`b=ka`

where k is a constant.

Substitute b=g, a=t and k=13.8182 in
`b=ka`.

`g=13.8182t`

Hence, the required equation is
`g=13.8182t`.

Check: Substitute t=5.5 in
`g=13.8182t`

`g=13.8182(5.5)`

`g\approx76.00`