Certainly! Let's break down the steps to create a linear function that models the total cost \( t \) for a single order of \( s \) pairs of shoes, given the costs mentioned.
1. Understand the Problem:
- Each pair of shoes costs [tex]$\$[/tex]59.99$.
- There is a flat rate shipping fee of [tex]$\$[/tex]8.95$ irrespective of the number of pairs of shoes purchased.
2. Identify the Components of the Linear Function:
- The cost of \( s \) pairs of shoes will be \( \$59.99 \times s \).
- The flat rate shipping fee is a constant \( \$8.95 \).
3. Formulate the Linear Function:
A linear function can be written in the form \( t(s) = ms + c \), where \( m \) is the rate of change and \( c \) is the y-intercept (or constant term).
- Here, \( m \), the rate of change, is \( \$59.99 \) because this is the cost per pair of shoes.
- The constant term \( c \) is the flat shipping fee, which is \( \$8.95 \).
4. Write the Function:
The total cost \( t \) for \( s \) pairs of shoes can be modeled by the linear function:
[tex]\[
t(s) = 59.99s + 8.95
\][/tex]
5. Conclusion:
Thus, the linear function that models the total cost \( t \) given \( s \) pairs of shoes is:
[tex]\[
t(s) = 59.99s + 8.95
\][/tex]
In summary, the total cost [tex]\( t \)[/tex] for a single order of [tex]\( s \)[/tex] pairs of shoes can be calculated using the function [tex]\( t(s) = 59.99s + 8.95 \)[/tex].
