Dependent & Independent Variables — From a Rule

Turn the rule into an equation, then use the equation to build the table and the graph, and to answer forwards and backwards.

1.
A kayak rental costs $20 plus $4 for each hour. Let c be the cost in dollars and h the number of hours.
a. Which is the independent variable? h, the hours c, the cost
b. Write an equation for c in terms of h.
c. Complete the table.
h 0 1 2 3 4 5
c
d. Plot the (h, c) pairs on the grid.
e. What does a rental of 10 hours cost?
How many hours can you rent for $48?
f. What does the cost for 0 hours tell you?
the fee to take the kayak out the price of each hour
2.
A ferry travels at a steady 10 miles per hour. Let d be the distance in miles and t the time in hours.
a. Which is the independent variable? t, the time d, the distance
b. Write an equation for d in terms of t.
c. Complete the table.
t 0 1 2 3 4 5
d
d. Plot the (t, d) pairs on the grid.
e. How far does the ferry travel in 7 hours?
How many hours does it take to travel 80 miles?
f. What does the number 10 in the equation tell you?
the miles covered in each hour the distance at the start
3.
A 200 mL bottle has a slow leak and loses 10 mL every minute. Let v be the volume left in mL and m the number of minutes.
a. Which is the independent variable? m, the minutes v, the volume
b. Write an equation for v in terms of m.
c. Complete the table.
m 0 4 8 12 16 20
v
d. Plot the (m, v) pairs on the grid.
e. How much is left after 15 minutes?
When is the bottle empty? minutes
f. What does the volume at 0 minutes tell you?
how full the bottle was to start how fast it leaks
4.
A printer prints 6 pages every minute. Let p be the number of pages and m the number of minutes.
a. Which is the independent variable? m, the minutes p, the pages
b. Write an equation for p in terms of m.
c. Complete the table.
m 0 1 2 3 4 5
p
d. Plot the (m, p) pairs on the grid.
e. How many pages does it print in 7 minutes?
How many minutes does it take to print 36 pages?
f. What does the number 6 in the equation tell you?
the pages printed each minute the pages printed before it starts
5.
A candle is 10 cm tall and burns down 2 cm every hour. Let c be the height in cm and t the time in hours.
a. Which is the independent variable? t, the time c, the height
b. Write an equation for c in terms of t.
c. Complete the table.
t 0 1 2 3 4 5
c
d. Plot the (t, c) pairs on the grid.
e. How tall is the candle after 2 hours?
When has the candle burned away? hours
f. What does the height at 0 hours tell you?
how tall the candle was to start how fast it burns