An online clothing company cells custom sweatshirts . The company charges $ 6.50 for each sweatshirt and a flat fee of $3.99 for shipping.
a) Write a linear function in the form y= mx + b that represents the total cost ,y in dollars , for a single order of x sweatshirts.
b) Describe how the linear function would change if the shipping charge applied to each sweatshirt.


Try to understand the difference when shipping charge are applied once per order no matter no of sweatshirts or to each sweatshirt ordered.

The correct answer is: (a) y = 6.5x + 3.99, (b) Increased

    SOL – Total cost = y
    No of sweatshirts = x
    (a) Acc. to the question, cost of 1 sweatshirt = $ 6.50
    Flat fee = $3.99
    Total cost = No of sweatshirts cross times Cost of each sweatshirt + Flat fee
    y = 6.5x + 3.99
    Here flat fee will act as an intercept and cost of each sweatshirt as slope.

    (b) If the shipping charges are applies to each sweatshirt then the cost of each sweatshirt = $ 6.50 + $3.99
    = $10.49
    Total cost = Cost of each sweatshirt  No of sweatshirts
    y = 10.49x
    As you can see slope of the graph when shipping charge was applied to each sweatshirt has increased as compared to the slope when shipping charge were applied once.
    This means total cost with respect to each sweatshirt has increased.