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7.01Applications of Linear Functions
Use each scenario to answer the questions that follow. You will have to choose the correct graph from the four choices given.
1.The phone company charges a flat rate of $25 per month. In addition, they charge $0.05 for each minute of service. Let x represent the number of minutes used each month.
(A)Define your variables.x =
y =
(B)Write an equation for the monthly charge based on the number of minutes of service per month.
The equation (in slope-intercept form) is y = x +
(C)Choose the correct graph from the choices below. Correct Graph:
(A)
(B)
(C)
(D)
(D)What will be the appropriate labels for the axes?
Label for x-axis:
Label for y-axis:
(E)Interpret the slope of the function.
(F)Interpret the y-intercept of the function.
(G)Estimate the charge for 400 minutes of service. Show your work below.
The charge for 400 minutes of service will be .
Show work here:
2.This spring, you are going to have to drain your swimming pool completely to replace the liner. Your pool holds a total of 24,000 gallons of water. When you begin draining, after one hour there are
23, 300 gallons of water remaining. After four hours, there are 21,200 gallons remaining in the pool.
(A)Define what each variable will represent.x =
y =
(B)Determine your two ordered pairs you will use to find the slope.
(,) and (,)
(C)Calculate the slope of the function.
m = / ()–() / =()–()
Fractional Answer / m =
Integer/Other Answer: m =
(D)Determine the equation of your function. (Hint: You are already given the y-intercept in the problem, which is the number of gallons in the pool before you pull the plug to drain)
The equation is y = x +
(E)What are the units for each axis?The units for the x-axis are .
The units for the y-axis are .
(F)Choose the correct graph of the function from the choices below. Correct Graph:
(A)
(B)
(C)
(D)
(G)What is the meaning of the y-intercept?
(H)How many gallons of water will be remaining after 16 hours? Show your work below.
After 16 hours, there will be gallons of water remaining in the pool.
Show work here:
(I)How many hours will it take for the pool to be completely drained? Round your answer to the nearest
hundredth. (Hint: This is the x-intercept of the function)
It will take roughly hours to completely drain the pool.