Question

a graph shows two points, (0,8) and (3,20) Colin charges a flat fee for babysitting plus an hourly fee. His total cost is represented on the graph. How can you represent this situation algebraically
y= ?x +?

Answer 1

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:

1. 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.

2. Calculate the slope (m):
- The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \):
\[
m = \frac{20 - 8}{3 - 0} = \frac{12}{3} = 4
\]

3. Identify the y-intercept (b):
- From the point (0, 8), we see that the y-intercept is \( b = 8 \).

4. 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.