To represent Colin's babysitting cost situation algebraically in the form \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), we can follow these steps:
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Identify the points given: (0, 8) and (3, 20).
- The first point (0, 8) suggests that when no hours are worked (x = 0), the total cost (y) is 8. This is the flat fee.
- The second point (3, 20) suggests that after working for 3 hours, the total cost is 20.
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Calculate the slope (m):
- The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \): \[ m = \frac{20 - 8}{3 - 0} = \frac{12}{3} = 4 \]
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Identify the y-intercept (b):
- From the point (0, 8), we see that the y-intercept is \( b = 8 \).
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Construct the equation:
- Now we can plug in the values into the linear equation format: \[ y = 4x + 8 \]
So, Colin's total cost for babysitting can be represented algebraically as:
\[ y = 4x + 8 \]
where \( x \) represents the number of hours babysat and \( y \) represents the total cost.
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