You take a trip to downtown Boston to walk the Freedom Trail with your family.
After you walk through the Bunker Hill Memorial, your family decides to take a taxi
to a restaurant for dinner. After 1 mile, the meter on the taxi says $4.75. It will cost
$8.25 to go 3 miles. The cost varies linearly with the distance that you traveled.
a. Write the particular linear function that models the cost of your trip as a
function of the distance traveled. Use the notation C d( ).
b. Write the function using improper fractions.
c. How much would it cost you to travel 10 miles in a taxi?
d. How far can you travel if you only have $10 to spend?
e. Calculate the cost-intercept. What does this number represent?
f. Plot the graph of this linear function. What is a suitable domain for
this problem? What is a suitable range?
g. What is the slope of the line? Show how to find it both graphically and
algebraically.
h. What does the slope of the line represent?
i. Write your own linear function word problem, and prove that it works
graphically and algebraically