Exploring Real-Life Linear Equations and Their Slopes

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write a linear equation to represent the total cost (C) in terms of miles driven (m). What is the slope and what does it represent?

• C = 20 + 0.20m; Slope = 0.20 (cost per mile)

• C = 20 + 0.10m; Slope = 0.10 (cost per mile)

• C = 20 + 0.15m; Slope = 0.15 (cost per mile)

• C = 15 + 0.15m; Slope = 0.15 (cost per mile)

Maria is saving money to buy a new bike. She currently has $50 and saves $10 each week. Write a linear equation to represent her savings (S) after w weeks. What is the y-intercept and what does it represent?

• S = 10w; y-intercept = 0 (no initial savings)

• S = 50 + 5w; y-intercept = 50 (initial savings)

• S = 50 - 10w; y-intercept = 50 (initial savings)

• S = 50 + 10w; y-intercept = 50 (initial savings)

A school is planning a field trip. The cost per student is $30, and there is a fixed cost of $200 for the bus. Write a linear equation for the total cost (C) in terms of the number of students (n). What is the slope and what does it represent?

• C = 30n; slope = 0

• C = 30n + 200; slope = 30

• C = 20n + 200; slope = 20

• C = 30n + 100; slope = 30

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 feet longer than twice the width. Write a linear equation to represent the length (L) in terms of the width (W). What is the slope of this equation?

• The slope of the equation is 0.5

• The slope of the equation is 3.

• The slope of the equation is 1.

• The slope of the equation is 2.

A phone company offers a plan that costs $25 per month plus $0.10 per text message. Write a linear equation for the total monthly cost (C) in terms of the number of text messages (t). What does the slope represent in this context?

• C = 25t + 0.10; the slope represents the total cost.

• C = 25 + 0.10t; the slope (0.10) represents the cost per text message.

• C = 0.10 + 25t; the slope represents the monthly fee.

• C = 0.10t; the slope represents the number of text messages.

A local gym charges a membership fee of $50 plus $5 for each class attended. Write a linear equation to represent the total cost (C) in terms of the number of classes (c). What is the y-intercept and what does it represent?

• C = 50 + 5c; y-intercept = 50, representing the membership fee.

• C = 50 + 10c; y-intercept = 50, representing the membership fee.

• C = 50c + 5; y-intercept = 5, representing the cost per class.

• C = 5 + 50c; y-intercept = 5, representing the total cost.

A bookstore sells notebooks for $2 each and has a fixed cost of $100 for supplies. Write a linear equation for the total revenue (R) in terms of the number of notebooks sold (n). What is the slope and what does it represent?

• R = 2n; slope = 2, representing revenue per notebook sold.

• R = 2n + 50; slope = 2, representing total cost per notebook sold.

• R = 5n; slope = 5, representing profit per notebook sold.

• R = 100 + 2n; slope = 100, representing fixed costs.

A taxi company charges a base fare of $3 plus $2 per mile. Write a linear equation to represent the total fare (F) in terms of miles traveled (m). What is the y-intercept and what does it represent?

• F = 3 + 2m; y-intercept = 3, representing the base fare.

• F = 3m + 2; y-intercept = 0, representing no fare.

• F = 2 + 3m; y-intercept = 2, representing the cost per mile.

• F = 5 + 2m; y-intercept = 5, representing an additional fee.

A factory produces toys at a cost of $15 each, plus a fixed cost of $500 for machinery. Write a linear equation for the total cost (C) in terms of the number of toys produced (t). What is the slope and what does it represent?

• C = 10t + 500; Slope = 10, representing the cost per toy.

• C = 15t; Slope = 0, representing no cost per toy.

• C = 15t + 500; Slope = 15, representing the cost per toy.

• C = 20t + 500; Slope = 20, representing the total cost.

A concert venue charges $100 for renting the space plus $10 per ticket sold. Write a linear equation for the total revenue (R) in terms of the number of tickets sold (n). What is the y-intercept and what does it represent?

• R = 100 + 5n; y-intercept = 100, representing half the rental cost.

• R = 100n; y-intercept = 1000, representing total ticket sales.

• R = 10n; y-intercept = 0, representing no cost.

• R = 100 + 10n; y-intercept = 100, representing the rental cost.