Question

Image shows a graph with the 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? (1 point)

Answer 1

y = {blank}x + {blank}

Answer 2

To represent Colin's babysitting cost situation algebraically, we can assume the total cost \( C \) can be expressed as a linear equation of the form:

\[
C = m \cdot h + b
\]

where:
- \( m \) is the hourly fee,
- \( h \) is the number of hours babysat,
- \( b \) is the flat fee (initial cost).

From the points given in the graph, we can identify:
- At \( h = 0 \) (0 hours), \( C = 8 \), indicating the flat fee \( b = 8 \).
- At \( h = 3 \) (3 hours), \( C = 20 \).

Now we can use these points to find the hourly fee \( m \).

From the second point where \( h = 3 \) and \( C = 20 \):
\[
20 = m \cdot 3 + 8
\]

Subtracting 8 from both sides gives:
\[
12 = 3m
\]

Dividing by 3 gives:
\[
m = 4
\]

Now we have both the flat fee and the hourly fee:
- \( b = 8 \) (flat fee)
- \( m = 4 \) (hourly fee)

Putting it all together, the algebraic representation of Colin's total cost can be written as:

\[
C = 4h + 8
\]

This equation describes how the total cost \( C \) varies based on the number of hours \( h \) he babysits.

Answer 3

Using the information we derived earlier, we can fill in the equation in the format \( y = mx + b \).

Based on our calculations:
- The slope \( m \) (hourly fee) is 4.
- The y-intercept \( b \) (flat fee) is 8.

So, the equation representing Colin's total cost for babysitting can be written as:

\[
y = 4x + 8
\]

In this equation:
- \( y \) represents the total cost,
- \( x \) represents the number of hours babysat.