To represent Colin's babysitting cost situation algebraically, we can assume the total cost \( C \) can be expressed as a linear equation of the form:
\[ C = m \cdot h + b \]
where:
- \( m \) is the hourly fee,
- \( h \) is the number of hours babysat,
- \( b \) is the flat fee (initial cost).
From the points given in the graph, we can identify:
- At \( h = 0 \) (0 hours), \( C = 8 \), indicating the flat fee \( b = 8 \).
- At \( h = 3 \) (3 hours), \( C = 20 \).
Now we can use these points to find the hourly fee \( m \).
From the second point where \( h = 3 \) and \( C = 20 \): \[ 20 = m \cdot 3 + 8 \]
Subtracting 8 from both sides gives: \[ 12 = 3m \]
Dividing by 3 gives: \[ m = 4 \]
Now we have both the flat fee and the hourly fee:
- \( b = 8 \) (flat fee)
- \( m = 4 \) (hourly fee)
Putting it all together, the algebraic representation of Colin's total cost can be written as:
\[ C = 4h + 8 \]
This equation describes how the total cost \( C \) varies based on the number of hours \( h \) he babysits.
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