2.6 Applications of Linear Functionsname
2.6 Applications of Linear FunctionsName:
● Recall – Average Rate of Change
Use the graph at the right to answer the following. Include the
unit rate in all of your answers.
a. Find the average rate for change for 0 to 400 minutes of usage.
b. Find the average rate of change for 400 to 600 minutes of usage.
c. Find the average rate of change for 0 to 600 minutes of usage.
d. What would your monthly cost be for using 175 minutes.
e. If your usage was 640 minutes, what would your monthly cost be?
● Writing and Solving Word Problems
Word problems in Slope-intercept form
Example 1: You are visiting Baltimore, MD and a taxi company charges a flat fee of $3.00 for using the taxi
and $0.75 per mile. How much would an 8-mile taxi ride cost?
a. What is the rate of change?What is the initial value?
b. Write an equation that you could use to find the cost of the taxi ride in Baltimore, MD.
Independent: Let x = ______
Dependent: Let y = ______
Equation:
c. Use your equation to answer the question with the correct units.
d. If your taxi ride cost $15, how many miles did you taxi travel?
Example 2: A student earns a 98% on a test for answering one question incorrectly and earns a 90% for
answering 5 questions incorrectly. What score would a student earn for answering 13 questions
incorrectly?
a. What is the rate of change?What is the initial value?
b. Write an equation modeling this situation.
Independent: Let x = ______
Dependent: Let y = ______
Equation:
c. Use your equation to answer the question with the correct units.
d. How many questions would a student answer incorrectly to earn a score of 66%?
Example 3: An airplane’s rate of decent in shown in the table below. Assume the plane continues at the
same rate of descent. The plane’s height and minutes above the ground are related to each
other. Find the altitude of the plane after 11 minutes.
# of minutes / 0 / 1 / 2 / 3altitude in feet / 30,000 / 28,000 / 26,000 / 24,000
a. What is the rate of change?What is the initial value?
b. Write an equation modeling this situation.
Independent: Let x = ______
Dependent: Let y = ______
Equation:
c. Use your equation to answer the question with the correct units.
d. How long does it take the plane to reach an altitude of 12,000 ft?
e. What if a violent storm is approaching and the plane had to increase its decent to 6000 miles every 2
minutes. How would this effect your equation?
Example 4:To make the perfect pizza, there should be pieces of pepperoni per slices of mushrooms.
If you put pieces of pepperoni, how many mushroom slices should you use?
a. What is the rate of change?What is the initial value?
b. Write an equation modeling this situation.
Independent: Let x = ______
Dependent: Let y = ______
Equation:
c. Use your equation to answer the question with the correct units.
Example 5: An appliance salesman is paid $50 every day plus some unknown amount for every appliance he
sells that day. One day, the salesman made $475 after selling 17 appliances. How much does he get
paid per appliance?
Practice
Write an equation for the given situation then answer the questions. Be sure to write your answers with the correct units.
1. A plumber charges $50 to make a house call. He also charges $25.00 per hour for labor. How much would
it cost for a house call that requires 2.5 hours of labor?
a. What is the constant rate?What is the initial value?
b. Write an equation that you could use to the amount a plumber charges for a house call based on the
number of hours of labor.
Independent: x = ______
Dependent: y = ______
Equation:
c. Use your equation to answer the question with the correct units.
d. If the bill from the plumber is $162.50, how many hours did the plumber work at your house?
2.Hannah's electricity company charges her $0.17 per kWh (kilowatt-hour) for electricity, plus a basic
connection charge of $15.00 per month.
a. Equation:
b. How much would Hannah’s bill be for 65 kWhs of usage?
c. How many kilowatt-hours of electricity did Hannah use if her bill was $440?
3. Lynn is tracking the progress of her tree’s growth. When planted the tree was 5 cm tall. 9 months later, the
tree is 18.5 cm tall. How tall will the tree be in 3 years?
a. What is the rate of change?What is the initial value?
b. Write an equation modeling this situation.
Independent: x = ______
Dependent: y = ______
Equation:
c. Use your equation to answer the question with the correct units.
d. How long will it take for the tree to reach a height of 75.5 cm?
4. The recipe for iced coffee at Starbucks suggests parts milk for every parts coffee. If a venti (the largest size) requires ounces of coffee, how many ounces of milk should be added?
a. What is the rate of change?What is the initial value?
b. Write an equation modeling this situation.
Independent: x = ______
Dependent: y = ______
Equation:
c. Use your equation to answer the question with the correct units.
5.To be a member of a gym you must pay a one-time $25 entry fee plus $10 per month. How much would it
cost to be a member for 1 year?
How many months of membership could you by for $365?
6.Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write
an equation for the water level, w, after d days. In how many days will the water level be 26 feet?
7. Your club is raising money by having a car wash. The relationship between the number of hours, h, it
takes to washc, cars is shown in the table.
Hours / Cars1 / 4
2 / 8
3 / 12
4 / 16
a. Write an equation modeling this situation.
b. How many cars can be washed in 12 hours?
c. How long will it take to was 100 cars?
8. . A rival club is also washing cars. The time it takes them to wash cars can also be modeled linearly.
Time washing (hr) / Cars washed3 / 18
5 / 30
6 / 36
8 / 48
a. Write an equation modeling this situation.
b. How many cars can be washed in 12 hours?
c. How long will it take to was 100 cars?
9. You are rereading your favorite book. The graph shows the number of pagesyou’ve read so far.
Assuming you really love this book and can’t put it down, how many pages will you have read after 17
hours?
If the book is 704 pages long, how long will it take you to complete the
book?
10. You start a tutoring company and have one student that you see once a week. You charge $15/hr. At the
end of five weeks, your business is worth $450. How much was your start-up investment (2 TI-84s, stick-
on glitter stars, etc.)?
11. An electrician’s fee for an emergency call out is $90 plus $20 for every 15 minutes spent on the job.
a. What is the electrician’s billing rate?
b. Can the electrician’s billing rate be stated as an hourly rate? What would it be?
c. Write an equation using the rate from a. or the hourly rate from b.
d. Use your equation to calculate the cost of a 45 minute repair.
12. As you drive to a football game, the number of kilometers you are away from home depends on the
number of minutes you have been driving. Suppose you are 8 km from homewhen you have been driving
for 10 minutes, and 11 km from home when you have been driving for 15 minutes. Predict your distance
from home after driving for 20 minutes.
a. What is the rate of change and what does it represent.
b. Write an equation in slope-intercept form then use your equation to answer the question.
c. When you are 18 km from home, how many minutes have you been traveling?
13. A computer repair service charges $50 for diagnosis and $35 an hour for repairs. Let x be the number of
hours it takes to repair a computer. Let y be the cost of repairs in dollars.
a. Write an equation for this situation.
b. Which quadrant(s) would be used to graph this situation?
Why?
c. For the grid below, determine a scale for the x- and y-axis. Label the x- and y-axis using the definitions of
the variables. Graph your equation.
(tip: use the table in your calculator to set the scale and select points for an accurate graph)
d. What is the domain?
e. What is the range?
14. The graph shows the altitude of a hot-air balloon during its linear descent. What is the equation of
descent in slope-intercept form?
a. What is the rate of change?
0
5
15
b. Complete the table to find
the initial value.
c. Equation:
