An online clothing company sells custom sweatshirts. The company charges $6.50 for each sweatshirt and a flat fee of $3.99 for shipping.

Question

a. Write a linear function in the form y = mx + b that represents the total
cost, y, in dollars, for a single order of & sweatshirts.
b. Describe how the linear function would change if the shipping charge applied to each sweatshirt.

Answer 1

a. In the given problem, the total cost \( y \) for ordering \( x \) sweatshirts can be represented by the linear function:

\[ y = mx + b \]

Here:

• \( m \) is the cost per item, which is $6.50.
• \( x \) is the number of sweatshirts ordered.
• \( b \) is the flat shipping fee, which is $3.99.

Thus, substituting these values into the equation, we have:

\[ y = 6.50x + 3.99 \]

b. If the shipping charge applied to each sweatshirt (meaning there is an additional shipping cost for each sweatshirt ordered), the cost structure would change. The new shipping charge per sweatshirt would be added to the cost of the sweatshirts.

Assuming the shipping cost per sweatshirt is the same as the flat fee, the new cost per sweatshirt would be $6.50 + $3.99, resulting in:

\[ m' = 6.50 + 3.99 = 10.49 \]

Thus, the new linear function representing the total cost \( y \) for ordering \( x \) sweatshirts would be:

\[ y = 10.49x \]

In this case, there would no longer be a flat shipping fee; instead, the shipping cost would be factored into the unit price of the sweatshirts.