To represent Colin's babysitting cost algebraically, you can use the point-slope form of a linear equation.
We know that the total cost \( y \) consists of a flat fee plus an hourly fee times the number of hours worked \( x \). The points given on the graph are:
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(0, 8): This point indicates that when \( x = 0 \) (zero hours), the total cost \( y \) is 8. This means the flat fee is $8.
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(3, 20): This point indicates that when \( x = 3 \) (three hours), the total cost \( y \) is 20.
Now, we can determine the hourly fee. The change in cost from the first point to the second point can be calculated: \[ \text{Change in } y = 20 - 8 = 12 \] \[ \text{Change in } x = 3 - 0 = 3 \] So, the hourly fee \( m \) can be calculated as: \[ m = \frac{\text{Change in } y}{\text{Change in } x} = \frac{12}{3} = 4 \]
Now we can formulate the equation of the line. The total cost equation can be expressed as: \[ y = mx + b \] Where:
- \( m = 4 \) (the hourly rate)
- \( b = 8 \) (the flat fee)
Thus, the equation representing the situation is: \[ y = 4x + 8 \]
So, the correct representation is: \[ y = 4x + 8 \]
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