In the graph you mentioned, we have two points: \( (0,8) \) and \( (3,20) \). We can interpret these points in the context of Colin's babysitting service:
- The point \( (0, 8) \) indicates that when no hours are worked (0 hours), the total cost is $8. This represents the flat fee for babysitting.
- The point \( (3, 20) \) indicates that when 3 hours are worked, the total cost is $20.
We can find the equation of the line that represents the total cost (y) as a function of hours worked (x).
First, let's identify the slope (m) of the line using the two points:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 8}{3 - 0} = \frac{12}{3} = 4 \]
This means Colin charges $4 per hour.
Next, we can use the point-slope form to write the equation of the line. We already know the y-intercept (the flat fee) from the point (0, 8), which is 8.
Now we can write the equation of the line in slope-intercept form (y = mx + b):
\[ y = 4x + 8 \]
Thus, the total cost can be represented algebraically as:
\[ y = 4x + 8 \]
Where:
- \( y \) is the total cost.
- \( x \) is the number of hours worked.
- 4 is the hourly fee.
- 8 is the flat fee for babysitting.
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