Name: ____________________________________________________________ Writing a Linear Function Rule Notes Writing a rule from a table: 1. The table shows the length of a kudzu vine that has been growing in the woods. Length Month a. What is the rate of change? (in feet) 0 20 1 24 b. Write a Now-­‐Next rule for the length of the vine. 2 28 3 32 c. Write a function rule that can be used to calculate the length, 𝐿 , for any 4 36 month, 𝑚 . d. Calculate the length of the vine after 8 months. 2. John is a contestant on The Biggest Loser. The table below shows John’s weight. John’s Weeks a. What is the rate of change? Weight 0 345 b. Write a Now-­‐Next rule for the weight of the contestant. 1 335 2 325 c. Write a function rule that can be used to calculate John’s weight, J, for any week, 𝑤 . 3 315 4 305 d. Calculate John’s weight after 12 weeks. 3. Don works at a car washing service. His pay can be modeled by the function 𝑃 = 30 + 5𝑐, where 𝑃 represents the amount Don gets paid, and 𝑐 represents the number of cars he washes. a. Calculate the missing pieces of the table below. Cars Washed 0 1 2 3 4 5 10 12 Paycheck b. Use the words NOW and NEXT to describe Don’s paycheck if he washes an additional car. c. What is the rate of change for John’s paycheck? Explain what it means. 4. The height of a rollercoaster can be modeled by the function 𝐻 = 45 + 8𝑡, where 𝐻 represents the height of the coaster and 𝑡 represents the time it has been traveling. a. Calculate the heights of the coaster in the table. Time (s) 0 1 2 3 4 5 10 12 Height (ft) b. Use the words NOW and NEXT to describe the height of the coaster after each additional second. c. What is the rate of change for the height? Explain what it means. d. What is the y-­‐intercept? Explain what it means? 5. Desmond bought a new laptop for $800 on his credit card. He has to pay all of this back to his credit card company. He plans to pay $50 each month to pay off his debt. a. Calculate the amount owed after each month after Desmond bought the computer. Monthly Payments 0 1 2 3 4 5 10 12 Amount Owed (in $) b. Use the words NOW and NEXT to describe the amount owed after each additional month. c.
Write a rule that can be used to show the amount owed, 𝐴, after 𝑚 monthly payments. d. What is the rate of change? Explain what it means. e. What is the y-­‐intercept? Explain what it means. 6. After a big storm, Jesse’s pool had lost a lot of its water and he needed to refill it. The pool water was at 4.5 feet deep so Jesse started pumping water into it. The level rose by 0.5 feet every hour. a. Complete the table below for the water level. Time (hours) 0 1 2 3 4 5 10 12 Water Level (feet) b. Use the words NOW and NEXT to describe the water level after each hour. c. Write a rule that can be used to show the water level, 𝐿 , for each hour ℎ. d. What is the rate of change? Explain what it means. e. What is the y-­‐intercept? Explain what it means.