Question

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

The points on the graph are (0,8) and (3,20)

Answer 1

To represent Colin's babysitting charges algebraically, we can use the points provided on the graph. The points are (0, 8) and (3, 20), which represent combinations of hours worked (x) and total cost (y).

1. **Identify Variables**:
- Let \( x \) be the number of hours he babysits.
- Let \( y \) be the total cost of babysitting.

2. **Setting Up the Points**:
- The point (0, 8) indicates that when Colin babysits for 0 hours, the total charge is $8, which represents the flat fee.
- The point (3, 20) indicates that when he babysits for 3 hours, the total charge is $20.

3. **Calculate the Hourly Rate**:
We can find the hourly rate by finding the change in cost per change in hours:

Change in cost from (0, 8) to (3, 20):
\[
\Delta y = 20 - 8 = 12
\]
\[
\Delta x = 3 - 0 = 3
\]
\[
\text{Hourly rate} = \frac{\Delta y}{\Delta x} = \frac{12}{3} = 4
\]

4. **Formulate the Cost Equation**:
The total cost can be expressed as:
\[
y = \text{(flat fee)} + (\text{hourly rate} \times x)
\]
Using the flat fee from the first point (0, 8), which is $8, and the hourly rate of $4:
\[
y = 8 + 4x
\]

5. **Conclusion**:
Hence, the algebraic representation of Colin's babysitting charges is:
\[
y = 4x + 8
\]
This equation shows the total charge \( y \) as a function of the hours \( x \) he spends babysitting, with a flat fee of $8 and an additional $4 for each hour worked.