Understanding Slope and Intercept in Real-World Functions

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 slope and what does it represent in this context?

• C(m) = 50 + 0.10m; Slope = 0.10 (cost per mile)

• C(m) = 50 + 0.20m; Slope = 50 (cost per mile)

• C(m) = 50 + 0.20m; Slope = 0.20 (cost per mile)

• C(m) = 50 + 0.50m; Slope = 0.50 (cost per mile)

A gym charges a monthly membership fee of $30 and an additional $5 for each class attended. If you attend 10 classes in a month, what is the total cost? Write the linear function and identify the y-intercept.

• $50

• $100

• $60

• The total cost is $80.

A school is selling tickets for a play. The tickets cost $8 each, and there is a fixed cost of $100 for the venue. Write a linear equation to represent the total revenue (R) from ticket sales based on the number of tickets sold (t). What does the slope represent?

• R = 8t + 100

• R = 8t

• R = 8t - 100

• R = 100t - 8

A phone company offers a plan that costs $40 per month plus $0.10 per text message sent. If you send 150 text messages in a month, how much will your bill be? Write the linear function and calculate the total cost.

• $60

• $50

• $45

• $55

A delivery service charges a base fee of $15 plus $2 for each mile driven. Write a linear equation for the total charge (C) based on the distance (d) in miles. What does the y-intercept represent in this scenario?

• C = 2d; The y-intercept represents the delivery fee per mile.

• C = 15 + d; The y-intercept represents the cost of delivery without any miles driven.

• C = 15d + 2; The y-intercept represents the total cost for 1 mile.

• C = 15 + 2d; The y-intercept represents the base fee of $15.

A local bakery sells cupcakes for $3 each and has a fixed cost of $50 for ingredients. Write a linear function to represent the total sales (S) based on the number of cupcakes sold (c). What is the slope and what does it indicate?

• The slope is 3, indicating that each cupcake sold increases total sales by $3.

• The slope is 50, indicating that the total sales are fixed regardless of cupcakes sold.

• The slope is 0, indicating that selling cupcakes does not affect total sales.

• The slope is 5, indicating that each cupcake sold decreases total sales by $5.

A taxi company charges a flat rate of $2.50 plus $1.50 per mile. If you take a ride that is 5 miles long, how much will it cost? Write the linear function and interpret the slope.

• $7.50

• $12.50

• $15.00

• $10.00

A subscription service charges $10 per month plus a one-time setup fee of $25. Write a linear equation to represent the total cost (C) after m months. What does the y-intercept represent in this context?

• C = 15m + 25; y-intercept represents the total cost after 2 months.

• C = 25m + 10; y-intercept represents the monthly fee of $10.

• C = 10m + 25; y-intercept represents the setup fee of $25.

• C = 10m; y-intercept represents the total cost after 1 month.

A farmer sells apples for $2 per pound and has fixed costs of $100 for equipment. Write a linear function to represent the total income (I) based on the pounds of apples sold (p). What does the slope represent?

• I = 2p + 100; the slope represents the total cost per pound sold.

• I = 2p - 100; the slope represents the income increase per pound sold.

• I = 100p; the slope represents the fixed costs per pound sold.

• I = 2p - 50; the slope represents the profit per pound sold.

A concert venue has a fixed cost of $2000 for hosting an event and charges $50 per ticket sold. Write a linear equation for the total revenue (R) based on the number of tickets sold (t). What does the y-intercept indicate?

• R = 50t + 2000; y-intercept indicates the number of tickets sold.

• R = 50t - 2000; y-intercept indicates the fixed cost of $2000.

• R = 2000t + 50; y-intercept indicates the total revenue at zero tickets sold.

• R = 50t - 1000; y-intercept indicates the variable cost per ticket.