To represent the situation algebraically, we need to understand the relationship between the total cost \( y \) and the number of hours \( x \) Colin babysits.
From the information given, Colin charges a flat fee (which we'll call \( b \)) and an hourly fee (which we'll call \( m \)). The total cost can be expressed as:
\[ y = mx + b \]
Where:
- \( y \) is the total cost.
- \( x \) is the number of hours babysat.
- \( m \) is the hourly fee.
- \( b \) is the flat fee.
In your example, if we denote the flat fee by some number and the hourly fee as well, you would plug in those values. For instance, if the flat fee \( b \) is 10 dollars and the hourly fee \( m \) is 5 dollars, the equation would look like:
\[ y = 5x + 10 \]
You will need to interpret the graph to identify the slope (hourly fee) and y-intercept (flat fee) to write the specific equation for Colin's babysitting charges. If you can determine those values from the line graphed, you can substitute them into the equation.