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.
- Flat fee (y-intercept): The flat fee is $8 (from the point (0, 8)).
- 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.
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