Question

Jeri is a hairdresser. The table below shows the relationship between the number of clients she has per month, x, and her monthly revenue, f(x). Based on the relationship shown in the table, which function represents the situation?
x f(x)
12 0
20 800
30 1800

A.
f(x) = 4x + 720
B.
f(x) = 8x - 96
C.
f(x) = 12x - 144
D.
f(x) = 100x - 1200

Answer 1

The given data is

  x       f(x)
----  --------
12          0
20     800
30    1800

where
x = number of clients per month
f(x) = monthly revenue

A graph of the data is shown below.
Let the equation of the line be
y = mx + c

The x-intercept is 12, therefore
12m + c = 0              (1)

The line passes through (30, 1800) and (12,0). Therefore the slope is
m = 1800/(30-12) = 100       (2)

From (1), obtain
c = -12m = -12*100 = -1200

Therefore
y = 100x - 1200

Answer: D. f(x) = 100x - 1200