Activities

1. What is the slope of a linear function that passes between (2, 7) and (5, 12)?

2. What is the slope of a linear function that passes between (-4, 7) and (5,-6)?

3. In the equation y = 5 – x, by what value does y change when x increases by 1?

4. Malcolm’s basketball team eats pizzas at a rate of 4.5 per game. How many total pizza’s have they eaten before their 13^th game?

5. A tree was h₁ feet tall at the beginning of April and h₂ feet tall by the end of October, what expression would determine the average rate of growth, in feet/month, for that time period?

6. Jonah and his friends opened a box of cookies at 7:41PM, there were 48 cookies inside. At 7:50 there were only 12 cookies left in the box. At what rate were Jonah and his friends eating cookies?

7. Identify the section of the following graph that has a constant rate of change.
8. 

8. In the equation 3x – 5y = 2(x + 5) – 12 what is the rate of change?

9. Tina reads a 431-page book in 20 hours. What is the average rate that she reads in pages per hour?

10. Mr. Math can create 20 multiple-choice problems in 15 minutes. How long would it take for him to create 50 multiple-choice problems?

11. Marketa is paying off her $15,000 college loan at a rate of $200 per month. If Marketa wants to create a function to determine the amount of money she still needs to pay off based on the month, should her rate of change be positive or negative? Why?

12. The number of rabbits in a certain enclosure tends to double every 4 months. If the pen starts with 10 rabbits in January, how many will it have in May, September, and next January? Is this a constant rate of change, yes or no?

13. Tim’s neighbor is leaning a ladder against the brick wall of his house to complete some repairs. If the slope of the ladder is 7/2 and the base of the ladder is 7 feet from the base of the wall, how high up on the wall is the top of the ladder resting?

14. Robert’s bank balance in dollars is graphed as a function of months. What is the rate of change of his bank account, in dollars per month?

15. A function doubles the input and then decreases that value by 3. What is the rate of change of this function?

16. Determine if the following table represents a constant rate of change, yes or no. Explain your answer.

17. At what ages during a person’s lifetime is their height most likely to have a constant rate of change?

18. Describe how the rate of change is different between a vertical and horizontal line. Use the graph below in your explanation.

19. The slope of an average single-family house is described as 6/12 pitch, which means that there is 6 inches of rise for every 12 inches of horizontal distance on the roof. A house is 26 feet wide with a peak exactly in the center. The peak is exactly how much taller than the sides of the roof?

20. What is the constant rate of change of the following graph?

21. Ms. Stephanie was trying to get her students to think more deeply about how to determine the rate of change for a graph. In order to get them thinking, she switched the x and y axes. Find the slope of the line graphed here.

22. No matter what value is input into a function, the output always decreases by 25 when the input is added to three. What is the rate of change of this function?

23. Compare and contrast something that has a linear rate of change with something that has a non-linear rate of change.

24. Tasha is reading a book. After 2 hours of reading she has 226 pages left to read. After another 5 hours of reading she only has 141 pages left to read. Assuming Tasha reads at a constant rate, how many pages were in the book originally?

25. Two vehicles are traveling to the same town according to the graph below. The sports car is further away, but traveling at a rate of 65 miles per hour. Meanwhile, the pickup truck begins closer to the town but is only going 49 miles per hour. Which will arrive first to the town? Extension: how much time will elapse from when the first vehicle arrives until the second vehicle gets there?

Answer Key/Rubric

1. 5/3

2. -13/9

3. y decreases by 1

4. 54 pizzas

6. 4 cookies per minute

7. Identify the section of the following graph that has a constant rate of change.

8. m = 1/5

9. 21.55 pages per hour

10. 37.5 minutes

11. Negative, because she is decreasing the total amount of money she has to pay each time she makes a monthly payment.

12. May: 20 rabbits, September: 40 rabbits, next January: 80 rabbits. This is not a constant rate of change because every 4-month period has a different amount of new rabbits.

13. 24.5 feet

14. Decreasing $50 per month

15. m = 2

16. No, because although the output value increases by 6 for every new point, the input values are not increasing by 1 at the same time. For example, the rate of change between the first two points is 6, but the rate of change between the last two points is 3/2.

17. From the time that they are done with puberty until they begin to shrink some as a senior citizen. In other words, any time that they are not growing.

18. When you are discussing the rate of change of lines, it is helpful to think about the concept of rise over run. In the case of the horizontal line, the rise is always zero between any two points and so, regardless of the run; the rate of change is always zero. On the other hand, for the vertical line, the run is always zero. This means that the rise over run expression always simplifies to . Since this expression is undefined (you cannot divide by zero), the rate of change of a vertical line is always undefined. For the same reason, a vertical line is not a function.

19. The center of the roof is 6.5 feet above the sides of the roof

20. The graph does not depict a constant rate of change

21. m = -2

22. m = -25/3

23. The cost of purchasing several of the same items is considered a linear function. This means that if the item, lets say a can of soup, is $0.95, then each additional can of soup would increase your cost by $0.95. On the other hand, a person’s growth rate would be a non-linear function. No-one grows the exact same number of inches every year of their life.

24. 260 pages

25. The sports car will arrive first. Extension: The pickup truck will arrive in approximately 1 minute and 26 seconds.