Question

The linear function y=2x+28 models the average cost of a haircut in a certain city, where y, is the average price of a haircut x years after 2000. Find the slope for the model. Then describe what this means in terms of the unit rate of change in the average cost of a haircut over time.

Answer 1

Answer:

The slope of the model is $m = 2\,\frac{USD}{yr}$.

The value of the slope indicates that the average cost of a hair cut is increased by 2 US dollars each year.

Step-by-step explanation:

We have to notice that given function is a linear function, that is, a first order polynomial, whose standard form is described below:

$y =m\cdot x + b$

Where:

$m$ - Slope, dimensionless.

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$b$ - y-Intercept, dimensionless.

In this case, we use the linear function $y = 2\cdot x + 28$, where $x$ is the time after 2000, measured in years, and $y$ is the average cost of a hair cut. The slope of the model is $m = 2\,\frac{USD}{yr}$.

The value of the slope indicates that the average cost of a hair cut is increased by 2 US dollars each year.