Exploring Real-Life Linear Functions & Rate of Change

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear function to represent the total cost (C) in terms of miles driven (m). What is the rate of change?

• C(m) = 50 + 0.10m; Rate of change = 0.10

• C(m) = 50 + 0.50m; Rate of change = 0.50

• C(m) = 25 + 0.20m; Rate of change = 0.20

• C(m) = 50 + 0.20m; Rate of change = 0.20

A gym membership costs $30 to join and $15 per month. Write a linear equation for the total cost (C) after m months. How much will it cost after 6 months?

• $90

• $180

• $120

• $150

A phone plan costs $25 per month plus $0.10 per text message. If you send 50 text messages in a month, what is the total cost? What is the rate of change per text message?

• Total cost: $35; Rate of change per text message: $0.15

• Total cost: $25; Rate of change per text message: $0.05

• Total cost: $40; Rate of change per text message: $0.20

• Total cost: $30; Rate of change per text message: $0.10

A school is selling tickets for a play. The tickets cost $10 each, and they sold 150 tickets. Write a linear function to represent the total revenue (R) in terms of the number of tickets sold (t). What is the slope of this function?

• 15

• 20

• 5

• 10

A factory produces 200 units of a product in the first hour and increases production by 50 units each subsequent hour. Write a linear function for the total production (P) after h hours. What is the rate of change?

• P(h) = 50h + 100; Rate of change = 100

• P(h) = 150h + 50; Rate of change = 150

• P(h) = 200h; Rate of change = 200

• P(h) = 50h + 150; Rate of change = 50

A delivery service charges a base fee of $5 plus $2 per mile. If a delivery is 10 miles, what is the total cost? Write the linear function and identify the rate of change.

• $20

• $15

• $25

• $30

A gardener plants 10 trees in the first week and adds 5 trees each week thereafter. Write a linear equation for the total number of trees (T) after w weeks. What is the rate of change?

• T = 10w + 10; Rate of change = 10

• T = 5w + 10; Rate of change = 10

• T = 10w + 5; Rate of change = 10

• T = 5w + 5; Rate of change = 5

A bookstore sells notebooks for $3 each. If they sold 200 notebooks, write a linear function for the total sales (S) in terms of the number of notebooks sold (n). What is the slope of this function?

• The slope of the function is 6.

• The slope of the function is 3.

• The slope of the function is 200.

• The slope of the function is 1.

A taxi charges a $3 base fare and $2 per mile. If a ride is 15 miles, what is the total fare? Write the linear function and calculate the rate of change.

• $33

• $15

• $25

• $40

A local farmer sells apples for $2 per pound. If he sells 80 pounds, write a linear function for the total revenue (R) in terms of pounds sold (p). What is the rate of change?

• R(p) = 3p; Rate of change = 3

• R(p) = 2p; Rate of change = 2

• R(p) = 2.5p; Rate of change = 2.5

• R(p) = 1.5p; Rate of change = 1.5