Question

the cost of a service call to fix a washing machine can be expressed by the linear function \\(y = 45x + 35\\), where \\(y\\) represents the total cost and \\(x\\) represents the number of hours it takes to fix the machine. what does the slope represent?

the cost for each hour it takes to repair the machine
the cost for coming to look at the machine
the total cost for fixing the washing machine
the amount of time that it takes to arrive at the home to make the repairs

Explanation:

Identify the given linear function

Using the Slope-Intercept Form and Linear Equation Interpretation knowledge points

$$ y = 45x + 35 $$

where \(y\) is the total cost in dollars, and \(x\) is the number of hours of repair work.

Analyze the slope of the function

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK0
$$

The slope \(m = 45\) represents the rate of change of the total cost per hour of repair.

Interpret the meaning of the slope

Using the Linear Equation Interpretation knowledge point

$$ \text{Slope} = \frac{\Delta y}{\Delta x} = \frac{\text{Change in total cost}}{\text{Change in hours}} = 45\text{ dollars per hour} $$

This represents the cost for each hour it takes to repair the machine.

Answer:

• the cost for each hour it takes to repair the machine (Correct answer)
• the cost for coming to look at the machine
• the total cost for fixing the washing machine
• the amount of time that it takes to arrive at the home to make the repairs