Amanufacturing company builds construction machinery. it sells 10 machines for $18,100 and 20 machines for $26,600. which equation models the revenue, r(x), as a linear function of the number of machines built, x ?

select one:
a. r(x)=750x−10100
b. r(x)=450x+7200
c. r(x)=1200x−4500
d. r(x)=850x+9600

D. R(x) = 850x +9600

Selling 10 more machines increased revenue from $18100 to $26600, an increase of ...

... $26,600 -18,100 = $8,500

That is, the revenue increased by $8500/10 = $850 per machine.

Only one answer choice has this number in it:

... D. R(x) = 850x+9600

Check

R(10) = 850·10 +9600 = 8500 +9600 = 18,100 . . . . OK

R(20) = 850·20 +9600 = 17000 +9600 = 26,600 . . . . OK

Comment on answer selection

On multiple-choice questions, it is rarely necessary to work out the solution to the problem completely. Usually, it is sufficient to find the one number that discriminates between correct and incorrect answers.

In real life, answers are rarely multiple-choice. You are required to work the problem completely and to figure out how to tell if your answer is correct.

Here, we have worked the problem far enough to find the slope, the amount by which revenue increases when sales increases by 1 unit. The intercept can be found different ways. One of them is to see what number makes the revenue match for one of the "x" values:

... R(10) = 850·10 +b = 18100

... b = 18100 -8500 = 9600

so ...

... R(x) = 850x +9600

We can check this answer by computing R(20), as we have above.

it would be 6xy and -16xy.