Question

Activity 1 of 2 Part A A hardware store rents vacuum cleaners that customers may use for part or all of a day, up to 12 hours, before returning. The store charges a flat fee plus an hourly rate. Write a linear function f for the total rental cost of a vacuum cleaner.

Answer 1

Part A:

Based on the information of the table and by taking into account that an equation of a linear relation can be written as follow:

f(x) = mx + b

where m is the rate of change and b the y-intercept.

Use the following formula for the calculation of m:

m = (y2 - y1)/(x2 - x1)

where (x1,y1) and (x2,y2) are a pair of values of the table. Use:

(x1,y1) = (1 , 20)

(x2,y2) = (1.5 , 23)

m = (23 - 20)/(1.5 - 1)

m = 3/0.5

m = 6

the y-intercept can be found by using the following expression:

y - yo = m(x - xo)

where (xo,yo) is a point of the table. Use (xo,yo) = (1,20)

y - 20 = 6(x - 1)

solve the previous expression for y:

y = 6x - 6 + 20

y = 6x + 14

Hence. the linear relation is

f(x) = 6x + 14

Part B:

The interpretation of the previous function is that if x is the time, there is a charge of 6 dollars per hour, and the independent term is the flat flee, which is 14 dollars.