Activities

1. In the linear function y = 4 – x, what is the slope and what is the y-intercept?

2. The distance a car has traveled from Miami to Boston follows the equation , where m is the time spent traveling in minutes and d is the total distance traveled in miles. How many miles has Tiffany traveled if she has been in the car for 3 hours?

3. The equation m = 525w + 1220 describes the amount of money (m) in Ted’s bank account after (w) weeks of saving from his new job. What does the number 1220 represent in this situation?

4. If the cost to download songs from a certain website is $0.95 per song plus a one time admission fee of $2.50, write and use an equation to determine how many songs (s) you can purchase for $31.00.

5. The table below displays the amount of money in Jasir’s bank account after any number of years at his most recent job. Assuming he saved the same amount each year, how much money did Jasir start with?

6. Your school is selling tickets for the spring theatre performance. The equation t = 955 – 40d represents the amount of tickets (t) that are expected to be remaining (d) days after they first go on sale. What do the 955 and -40 represent in this situation?

7. An entrepreneur that you know buys a new pair of sneakers for $175 after waiting in line for 2 hours. The same pair of shoes can be sold for $215. Write an equation that could be used to determine how many pairs of shoes (S) the entrepreneur would have to sell in order to have a profit of $100. Use only the numbers from this problem in your equation.

8. Sales tax in Pennsylvania is currently 6%. Write a linear equation that would determine the total cost (T) of any taxable item that has a price tag of (p) dollars.

9. Andy is climbing up a very steep mountain in Colorado. His decent can be described by the equation f = 14,114 – 2350h where f is the number of feet above sea level and h is the time in hours Andy has hiked from the top of the mountain. Explain why it does not make sense for h to equal 7 in this equation.

10. Chris works after school making deliveries for a company in his hometown. He earns money according to the linear function m = 7d – 3, where d is the amount of deliveries Chris makes and m is the amount of money earned. Fill in the table below with 5 coordinate points that would be reasonable based on this situation.

11. Tammy bought a relatively new car that had only 2,563 miles on it. She plans to drive the car about 10,000 miles per year. Sketch a graph of the linear function which inputs the amount of years Tammy has owned the car and outputs the amount of miles the car has been driven.

12. The amount of new snow falling on Williamsport is described by the equation s = p + rh. In this equation, s stands for total snowfall, p is the previous snow on the ground, r is the rate of the current snowfall and h is the time, in hours, of the current snowfall. If after 5 hours of snow there were 2.5 inches of snow and after 9 hours there were 3.5 inches of snow, how much snow was on the ground before this storm began?

13. The graph below shows the relationship between the gallons of gas remaining in a car, and the distance that it can travel. Approximate, as accurately as possible, the gas mileage on the car described below?

14. Jim’s Workout Gym offers the following membership choices: one month for $32, two months for $39, six months for $67, or a year for $104. The cost follows a linear relationship. Write an equation that could be used to figure out the cost (C) of m months?

15. Ethan has $11.00 in quarters, q, and dimes, d. Create an equation that could represent the number of quarters and dimes that Ethan has?

16. The graph below displays the distance (d) of Jabrina from her friend Jared after some time (t). Describe how the distance between the two friends is changing over time.

17. Fill in the missing value in the linear function table below.

18. The graph below depicts the amount of money in Juliet’s bank account over a span of time. Describe in as much detail as you can, what is happening with Juliet’s money.

19. The equation used to determine the price of a new LCD TV is 1.06(0.85c) = p, where c is the original cost and p is the price you have to pay after a discount and sales tax. How much money are you saving because of the discount if the original price for the TV is $600?

20. A certain cell phone provider charges $40 per month plus $7.50 for each Gigabyte of data for each cell phone user in a family. Your mother used x Gigabytes of data, your sister uses twice as much data as your mom and you used twice as much data as your sister last month. If the family spent $92.50 on cell phones last month, how many Gigabytes of data did you use? Write an equation that can be used to determine your solution.
    
    

21. The graph below describes a person’s distance from a fixed starting point on a straight track. Describe the rate and direction the person is walking for the following times.

1. 0 to 10 seconds:

2. 10 to 15 seconds:

3. 15 to 40 seconds:

4. 40 to 55 seconds:

How far away from where they started did they finish?

23. Two planes, 2,400 miles apart, start flying towards each other at different speeds. The first plane flies 50 mph faster than the other. They meet after 5 hours. What was the speed of each plane?
    
    
24. Marc bought 7 new shirts for school on Wednesday. On Thursday his brother “borrowed” half of Marc’s shirts. On Friday Marc had 13 shirts. Write an equation that could be used to determine how many shirts Marc had the previous Tuesday.
    
    
25. The equation b – y = ax is graphed below. What could be the values of a and b?

25. The sum of 5 consecutive odd integers is 95. What linear equation could be solved to determine the first integer?

Answer Key/Rubric

1. The slope is m = -1 and the y-intercept is b = 4.

2. 195 miles

3. The amount of money that was in his bank account before saving from his new job.

4. 0.95s + 2.5 = 31, s = 30 songs can be purchased

5. $2080.00

6. The 955 represents the amount of seats in the auditorium and the -40 represents the amount of tickets that are expected to be sold each day.

7. S(215 – 175) = 100

8. T = p + 0.06p = 1.06p

9. If h would equal 7, then the output would be -2336 feet above sea level. This would mean that Andy hiked not only down the entire mountain, but also over 2000 feet below sea level.

10. The following numbers do make sense. You could not choose to input any negative numbers or zero into this function, as those values would not be logical.

11. Miles = 10,000(years) + 2563

12. 1.25 inches of snow

13. 20 miles per gallon

14. C = 7m + 25

15. 0.25q + 0.10d = 11

16. Jabrina and Jared are remaining exactly the same distance apart
    
    
17. 
    

18. Juliet started with a little bit of money and has been gradually losing money over time. She has by now lost about twice the amount of money she started with.

19. $95.40The equation used to determine the price of a new LCD TV is 1.06(0.85c) = p, where c is the original cost and p is the price you have to pay after a discount and sales tax. How much money are you saving because of the discount if the original price for the TV is $600?

20. 4 GB, 40 + 7.5(x + 2x + 4x) = 92.50, then multiply x by four to get your Gigabyte total

21. 
    
    1. 0 to 10 seconds: forward at 6 meters per second

2. 10 to 15 seconds: standing still for 5 seconds

3. 15 to 40 seconds: backwards at 4 meters per second past the original starting point

4. 40 to 55 seconds: forwards at meters per second

     They stopped at the same place they started

22. Plane 1: 265 mph, Plane 2: 215 mph

24. Various answers including a= -5, b = 5
    
    
25. x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 95, x = 15