Question

a graph shows two points, (0,8) and (3,20)
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

Answer 1

To represent Colin's babysitting charges algebraically based on the points given on the graph, we can interpret the points (0, 8) and (3, 20) as follows:

- The first point, (0, 8), indicates that when Colin works for 0 hours, the total cost is \$8. This implies that he charges a flat fee of \$8, regardless of hours worked.
- The second point, (3, 20), indicates that when Colin works for 3 hours, the total cost is \$20.

From these points, we can derive the hourly charge.

1. **Flat fee (y-intercept)**: The flat fee is \$8 (from the point (0, 8)).
2. **Hourly fee (slope)**: We can calculate the hourly rate using the two points.

The formula for the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:
\[
m = \frac{y₂ - y₁}{x₂ - x₁}
\]

Using the points (0, 8) and (3, 20):
- (x₁, y₁) = (0, 8)
- (x₂, y₂) = (3, 20)

Now substituting the values in:
\[
m = \frac{20 - 8}{3 - 0} = \frac{12}{3} = 4
\]

This means Colin charges \$4 per hour.

Now, we can express the total cost (C) as a function of the number of hours worked (h):
\[
C(h) = 8 + 4h
\]

Thus, the algebraic representation of Colin's babysitting charges is:
\[
C(h) = 8 + 4h
\]
where:
- \(C(h)\) is the total cost,
- 8 is the flat fee,
- 4 is the hourly rate,
- \(h\) is the number of hours worked.