Question

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

A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)
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

The equation that can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked is; E = 7.5 h

How to solve direct variation problems?

The points (0, 0) and (12, 90) lie on the graph of the direct variation function.

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

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

Slope = (y₂ - y₁)/(x₂ - x₁)

Thus;

Slope = (90 - 0)/(12 - 0)

Slope = 7.5

We are told that the total earnings E, varies directly as the number of hours worked ,h. Thus, the mathematical relationship is;

E ∝ h

Thus, using constant of proportionality, we have;

E = kh

where k is constant of proportionality which is the slope. Thus;

E = 7.5h

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Answer 2

Answer:

B. E = 7.5h

Step-by-step explanation:

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