Question

Tamara was asked to write an example of a linear functional relationship. She wrote this example:

• My baby-sitting service charges an initial $5.00 fee plus an additional $6.50 per hour.
Complete the table below to create an example of the baby-sitting rate.
Total Hours Cost
1
2
State whether Tamara's example represents a linear functional relationship. Explain your reasoning.

Answer 1

Tamara's example is in fact an example that represents a linear functional relationship.

• This is because the cost of baby-sitting is linearly related to the amount of hours the nany spend with the child: the more hours the nany spends with the child, the higher the cost of baby-sitting, and this relation is constant: for every extra hour the cost increases at a constant rate of $6.5.

• If we want to represent the total cost of baby-sitting in a graph, taking the variable "y" as the total cost of baby-sitting and the variable "x" as the amount of hours the nany remains with the baby, y=5+6.5x (see the graph attached).
• The relation is linear because the cost increases proportionally with the amount of hours ($6.5 per hour).
• See table attached, were you can see the increses in total cost of baby sitting (y) when the amount of hours (x) increases.