Question

a plumber charges a $45 fee to make a house call and then $25 for each hour of labor. the plumber uses an equation in the form \\(y = mx + b\\) to determine the amount to charge each customer.

what is the value of \\(m\\) in the equation?

\\(m = \\$\\)

Explanation:

Identify the variables and equation form

Using the Slope-Intercept Form knowledge point

$$ y = mx + b $$

where \(y\) represents the total charge, \(x\) represents the hours of labor, \(m\) represents the rate of change (hourly rate), and \(b\) represents the initial value (one-time fee).

Determine the rate of change

Using the Rate of Change knowledge point
The problem states the plumber charges \$25 for each hour of labor. This hourly rate is the constant rate of change:

$$ m = 25 $$

Determine the initial value

Using the Initial Value of Linear Function knowledge point
The plumber charges a flat \$45 fee to make a house call. This one-time fee is the initial value:

$$ b = 45 $$

Formulate the final equation

Using the Slope-Intercept Form knowledge point

$$ y = 25x + 45 $$

Thus, the value of \(m\) is 25.

Answer:

A plumber charges a \$45 fee to make a house call and then \$25 for each hour of labor. The plumber uses an equation in the form \(y = mx + b\) to determine the amount to charge each customer.

What is the value of \(m\) in the equation?

\(m = \$\) <blank>25</blank>