Question

(HELP NEEDED ASAP!!!)The graph represents the direct variation function between earnings in dollars and hours worked. Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked? E = 1.5h E = 7.5h E = 13h E = 15h

Answer 1

Option 2 - E=7.5h

Explanation:

Given: The graph represents the direct variation function between earnings in dollars and hours worked.

To find : Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?

Solution :

First we examine the graph,

The graph shows the linear equation.

The points (0,0) and (4,30) lie on the graph of the direct variation function.

We can use these points to determine the constant of proportionality which is the slope,

Formula to find slope is

`m=(y_2-y_1)/(x_2-x_1)`

`m=(30-0)/(4-0)`

`m=(30)/(4)`

`m=(15)/(2)=7.5`

The total earnings E, varies directly proportional to the number of hours worked h.

`E \propto h`

`E = kh`

where k is the constant of proportionality.

k=7.5

Substitute, in E

`E = 7.5h`

Therefore, Option 2 is correct.

Answer 2

ANSWER


`E=7.5h`

EXPLANATION

The points

`(0,0)`
and


`(12,90)`

lie on the graph of the direct variation function.

We can use these points to determine the constant of direct variation which is also called the constant of proportionality.

This constant of proportionality is the slope, which can be found using the formula,


`slope=(y_2-y_1)/(x_2-x_1)`

This implies that,


`slope = (90 - 0)/(12 - 0)`


`slope = 7.5`

Since the total earnings E, varies directly as the number of hours worked ,h,we can write the mathematical relation,


`E \propto \: h`

The equation of the direct variation function is given by

`E = kh`

where k is the constant of proportionality.

We substitute this value to get,


`E = 7.5h`