Question

linearset2: problem 7
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(1 point) the linear function c(y)=4y + 30 models the average cost of a haircut in a certain city, where c is the average price of a haircut y years after 2000. find the slope for the model. then describe what this means in terms of the rate of change in the average cost of a haircut over time.
a) the slope =

b) the average cost of a haircut in this city choose one at a rate of per after 2000.
you must include one symbol for the units in the second blank (as well as a numerical value) and one word for the units in the third blank.
note: you can earn partial credit on this problem.
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Explanation:

Step1: Identify slope - intercept form

The linear function is $C(y)=4y + 30$, which is in the form $y=mx + b$ where $m$ is the slope.

Step2: Determine the slope

For $C(y)=4y + 30$, the coefficient of $y$ is 4, so the slope $m = 4$.

Step3: Interpret the slope

The slope represents the rate of change. Since $y$ is years after 2000 and $C$ is cost, the average cost of a haircut increases at a rate of $\$4$ per year after 2000.

Answer:

a) The slope = 4
b) The average cost of a haircut in this city increases at a rate of $\$4$ per year after 2000.