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

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.