Question

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? (3,20) (0,8)

Answer 1

To represent Colin's babysitting charges algebraically, we can identify the components of the linear relationship based on the points given:

1. **Flat Fee (y-intercept)**:
- From the point (0, 8), we see that when the hours (x) are 0, the total cost (y) is 8. This indicates that the flat fee is $8.

2. **Hourly Fee (Slope)**:
- The point (3, 20) tells us that when Colin babysits for 3 hours, the total cost is $20.
- To find the hourly fee, we can calculate the change in total cost with respect to the change in hours.
- We have two points: (0, 8) and (3, 20). The change in total cost (Δy) is \( 20 - 8 = 12 \) and the change in hours (Δx) is \( 3 - 0 = 3 \).
- The hourly fee (slope) can be calculated as:
\[
\text{slope} = \frac{Δy}{Δx} = \frac{12}{3} = 4
\]
- This means Colin charges $4 per hour.

3. **Algebraic Representation**:
- Combining the flat fee and the hourly rate, the total cost (C) as a function of hours (h) can be represented by the equation:
\[
C(h) = 8 + 4h
\]

Thus, the algebraic representation of Colin's babysitting charges is:
\[
C(h) = 8 + 4h
\]
where \( C(h) \) is the total cost for \( h \) hours of babysitting.