Question

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? Fill in the blanks with the correct values. y = __ x + __
3 ,20
8,4
0,8
4, 8

Answer 1

To represent Colin's babysitting costs algebraically, we need to identify the flat fee (the y-intercept) and the hourly fee (the slope) from the points on the graph provided.

Let's analyze the points:

1. **(0, 8)**: This point indicates that when no hours are worked (x = 0), the total cost (y) is 8. This means the flat fee is 8.
2. **(3, 20)**: This point indicates that after 3 hours of babysitting, the total cost is 20.
3. **(8, 4)**: This point shows that after 4 hours, the cost is 8.
4. **(4, 8)**: This seems inconsistent since it would imply that at 4 hours, the cost remains the same as the flat fee.

Let's calculate the hourly rate between the first two points (0, 8) and (3, 20):
- Change in y = 20 - 8 = 12
- Change in x = 3 - 0 = 3
- Slope (hourly fee) = Change in y / Change in x = 12 / 3 = 4.

Thus, the hourly fee is 4.

Now we have enough information to form the equation:
- The y-intercept (flat fee) is 8, and the slope (hourly fee) is 4.

The equation is written in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

So, the final equation is:
\[ y = 4x + 8. \]

Filling in the blanks:
\[ y = 4x + 8. \]