Solve the problem.
-Suppose that a sales person observes that if an item is priced at $8 per item then 10 items are sold. Find a linear function f(x) = mx + b whose input is the number of hours that the plumber works
And whose output is the corresponding cost for the house call. If 8 items are sold for $10 per item
Then use the function to model the number y of items sold for x dollars per item.
A) f(x) = x + 18
B) f(x) = -x + 18
C) f(x) = x + 2
D) f(x) = -x + 2

Question

Quizplus · Accepted Answer

From the given information, we know that the sales person observes that if an item is priced at $8 per item then 10 items are sold. This implies that the cost of 10 items is $8 x 10 = $80. This gives us the equation: 
10 = 8m + b

We are also given that 8 items are sold for $10 per item. This implies that the cost of 8 items is $10 x 8 = $80. Using the equation above, we can solve for b:
10 = 8m + b 
10 = 8m + 80 
b = -70

Therefore, the linear function is f(x) = -x + 18, since the cost for x number of items is given by the equation:
f(x) = -x + 18x 
To model the number of y items sold for x dollars per item, we can rearrange the equation:
x = y / 8 
Substituting this into the linear function gives:
f(y) = -(y/8) + 18

Solve the Problem. -Suppose That a Sales Person Observes That If an Item