Question

The graph below represents an employee's earnings based on units sold. What can be interpreted from the slope of this graph?

A.
The employee earns an additional $100 for every one unit sold.

B.
The employee earns an additional $100 for every ten units sold.

C.
The employee earns an additional $1,000 for every one unit sold.

D.
The employee earns an additional $31,000 for every ten units sold.

Answer 1

A

Explanation:

From inspection of the graph, we can see that every time the x-value increases by 10, the y-value increases by 1000.

So, the employee earns an additional $1000 for every 10 units sold.

To calculate how much the employee earns for every 1 unit sold, divide $1000 by 10:

1000 ÷ 10 = 100

Therefore, the employee earns an additional $100 for every one unit sold.

Proof

This can be proved by calculating the slope (gradient) of the graph:

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

where
`\sf (x_1,y_1)` and
`\sf (x_2,y_2)` are two points on the line

When picking the two points, remember that the y-values are in thousands of dollars.

Two points on the line:

(0, 30000) and (20, 32000)

Substituting these into the formula:

`\sf \implies slope=(32000-30000)/(20-0)=(2000)/(20)=100`

Therefore, the employee earns an additional $100 for every one unit sold.