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Linear functions

Find the slope from an equation

The graph shows the total cost C, in dollars, that a customer pays for n pounds of coffee from an online coffee merchant. The total cost includes a fixed fee for shipping.

a) What does the ordered pair (2, 13) mean?
b) How much does it cost to order 4 pounds of coffee?
c) Peter pais \$18 for an order. How many pounds of coffee did e order?
d) Ignoring the shipping cost, How much does each pound of coffee cost?
e) What is the shipping cost for each order?
f) Predict the cost to order 12 pounds of coffee.

a) The ordered pair (2,13) means that an order for 2 pounds of coffee costs \$13.
b) From the graph, we see that the cost to order 4 pounds of coffee is \$23.
c) From the graph, we see that \$18 corresponds to 3 pounds of coffee.
d) We see 13-8=5, 18-13=5, 23-18=5, and 28-23=5. The cost for an additional pound is \$5. So each pound of coffee cost \$5.
e) It costs \$8 to order 1 pound of coffee. Each pound of coffee costs \$5. The shipping cost is the difference: \$8-\$5=\$3.
f) We represent the cost (C) as a function of the number pounds (n) of coffee. The graph leads to the following table of ordered pairs:

 n 1 2 3 4 5 C 8 13 18 23 28

The cost 8, 13, 18, 23, 28,... are generalized by the equation C(n)=5n+3. The cost to order 12 pounds of coffee is C(12)=5·12+3=60+3=\$63.