Question

(3,20) (0,8) 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?

(1 point)
y= x+

Answer 1

To represent Colin's babysitting cost algebraically, you can use the point-slope form of a linear equation.

We know that the total cost \( y \) consists of a flat fee plus an hourly fee times the number of hours worked \( x \). The points given on the graph are:

1. (0, 8): This point indicates that when \( x = 0 \) (zero hours), the total cost \( y \) is 8. This means the flat fee is $8.

2. (3, 20): This point indicates that when \( x = 3 \) (three hours), the total cost \( y \) is 20.

Now, we can determine the hourly fee. The change in cost from the first point to the second point can be calculated:
\[
\text{Change in } y = 20 - 8 = 12
\]
\[
\text{Change in } x = 3 - 0 = 3
\]
So, the hourly fee \( m \) can be calculated as:
\[
m = \frac{\text{Change in } y}{\text{Change in } x} = \frac{12}{3} = 4
\]

Now we can formulate the equation of the line. The total cost equation can be expressed as:
\[
y = mx + b
\]
Where:
- \( m = 4 \) (the hourly rate)
- \( b = 8 \) (the flat fee)

Thus, the equation representing the situation is:
\[
y = 4x + 8
\]

So, the correct representation is:
\[
y = 4x + 8
\]