Question

Use the image to answer the question.

A line graph which shows X-axis ranging from 0 to 15 in increments of 5 and y-axis ranging from 0 to 30 in increments of 10. two poitn s are marked on the line... 3,20 and 0,8

Colin charges a flat fee for babysitting plus an hourly fee. His total cost is represented on the graph. How can you represent this situation algebraically?

(1 point)

Answer 1

To represent Colin's total cost for babysitting algebraically, we can use a linear equation of the form:

\[ C = mx + b \]

where:
- \( C \) is the total cost,
- \( m \) is the hourly fee (slope),
- \( x \) is the number of hours babysat,
- \( b \) is the flat fee (y-intercept).

From the points marked on the graph, we have:
1. The point (3, 20) indicates that after 3 hours, the total cost is $20.
2. The point (0, 8) suggests that when no hours are worked, the cost is a flat fee of $8.

Given that when \( x = 0 \), \( C = 8 \), we know that \( b = 8 \).

Now to find the slope \( m \):
Using the two points (0, 8) and (3, 20):
- The change in cost (\( \Delta C \)) is \( 20 - 8 = 12 \).
- The change in hours (\( \Delta x \)) is \( 3 - 0 = 3 \).

Thus, the slope \( m \) is:
\[ m = \frac{\Delta C}{\Delta x} = \frac{12}{3} = 4 \]

Now we can write the equation:
\[ C = 4x + 8 \]

This equation represents Colin's total cost for babysitting, where he charges a flat fee of $8 plus an hourly fee of $4 per hour.