Question

A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $10 million after 4 years, as shown in the graph.

Which equation most closely represents the line depicted in the graph?

A. f(x) = −10x + 4
B. f(x) = 15/2x - 20
C. f(x) = 10x − 4
D. f(x) = 2/15x - 20

Answer 1

B. f(x) = 15/2x - 20

Explanation:

Hi there!

All of the given functions are organized in slope-intercept form:

`y=mx+b` where m is the slope of the line and b is the y-intercept. The y-intercept is also the value of y where the line crosses the y-axis.

Notice how in the graph, the line crosses the y-axis at y = -20. This means that the y-intercept (b) is -20.

`y=mx-20`

We know now that the answer is either B or D.

In the graph, the line crosses the point (4,10). Let's find f(4) of both the functions given in B and D and see which answer is equal to 10.

Function B:

`f(x) = \displaystyle(15)/(2)x - 20\\\\f(4) = \displaystyle(15)/(2)(4) - 20\\\\f(4) = 30 - 20\\\\f(4) = 10`

Therefore, because f(4) is equal to 10 for function B, B is therefore the correct answer.

I hope this helps!