Question

A cleaning service charges an initial fee plus an hourly rate.
The total cost for different numbers of hours, including the initial fee, is shown on the graph. Find and interpret the rate of change and initial value. Then write the equation of the
function in the form y = mx + b.

Answer 1

Answer:

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Step-by-step explanation:

To find the rate of change and the initial value from the graph, we can identify two points and calculate the slope (rate of change) and the initial value (y-intercept).

Let's choose two points from the graph, (0, initial fee) and (h, total cost for h hours).

The rate of change (m) represents the cost per hour, and the initial value (b) represents the initial fee.

Let's interpret the values and then find the equation of the function:

1. **Rate of Change (m)**:

The rate of change represents the cost per hour, which is the slope of the line. We can calculate it using the formula:

\[ m = \frac{\text{change in cost}}{\text{change in hours}} \]

2. **Initial Value (b)**:

The initial value represents the initial fee, which is the y-intercept of the line.

3. **Equation of the Function (y = mx + b)**:

Once we have the rate of change and the initial value, we can write the equation of the function in slope-intercept form.

Let's perform these calculations using the provided graph. Once you provide the values, I can help you interpret and write the equation of the function.