Exploring Linear Functions: Slope and Intercept in Real Life

A car rental company charges a flat fee of $20 plus $0.15 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?

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

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

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

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

A gym charges a monthly membership fee of $30 and an additional $5 for each class attended. Write the linear function for the total cost (C) based on the number of classes (c) attended. What does the y-intercept represent in this context?

• C = 5c; y-intercept represents the initial cost of attending classes.

• C = 5 + 30c; y-intercept represents the cost per class.

• C = 30c + 5; y-intercept represents the total cost of classes.

• C = 30 + 5c; y-intercept represents the membership fee of $30.

A phone plan costs $25 per month plus $0.10 for each text message sent. If you send 50 text messages in a month, what is your total cost?

• $30

• $35

• $25

• $40

A delivery service charges a base fee of $10 and $2 for each mile driven. If you need to calculate the cost for a delivery of 15 miles, what is the total cost?

• $25

• $40

• $30

• $50

A school is selling tickets for a play. The tickets cost $8 each, and there is a one-time fee of $50 for the venue. Write a linear function for the total revenue (R) based on the number of tickets sold (t). What does the slope represent?

• R = 50t + 8; the slope represents the total cost of the venue.

• R = 8t + 50; the slope represents the revenue per ticket sold.

• R = 8t; the slope represents the total number of tickets sold.

• R = 50 + 8t; the slope represents the fixed cost of the venue.

A taxi company charges a base fare of $3 and $2 for each mile driven. If you take a ride that costs $15, how many miles did you travel?

• 6 miles

• 7 miles

• 5 miles

• 4 miles

A subscription service charges $10 per month plus a one-time setup fee of $20. Write the linear function for the total cost (C) based on the number of months (m) subscribed. What does the y-intercept indicate?

• C(m) = 10m + 10; The y-intercept indicates a discount on the setup fee.

• C(m) = 10m; The y-intercept indicates the total cost after one month.

• C(m) = 10m + 20; The y-intercept indicates the one-time setup fee of $20.

• C(m) = 5m + 20; The y-intercept indicates the monthly fee of $10.

A farmer sells apples for $2 per pound and has a fixed cost of $50 for equipment. Write a linear function for the total revenue (R) based on the pounds of apples sold (p). What does the slope represent in this scenario?

• R(p) = 50p; the slope represents the number of pounds sold.

• R(p) = 2p; the slope represents the price per pound of apples.

• R(p) = 50 + 2p; the slope represents the total cost of apples.

• R(p) = 2p + 50; the slope represents the fixed cost of equipment.

A concert venue has a seating capacity of 500 and charges $50 per ticket. If they sell all the tickets, what is the total revenue? Write the linear function and identify the slope and intercept.

• Total revenue is $20000. The linear function is R(x) = 40x with a slope of 40 and a y-intercept of 0.

• Total revenue is $30000. The linear function is R(x) = 60x with a slope of 60 and a y-intercept of 0.

• Total revenue is $15000. The linear function is R(x) = 30x with a slope of 30 and a y-intercept of 0.

• Total revenue is $25000. The linear function is R(x) = 50x with a slope of 50 and a y-intercept of 0.

A local bakery sells cupcakes for $3 each and has a fixed cost of $15 for ingredients. Write a linear function for the total cost (C) based on the number of cupcakes (c) sold. What does the y-intercept represent in this situation?

• C(c) = 2c + 15; y-intercept represents the variable cost per cupcake.

• C(c) = 3c + 15; y-intercept represents the fixed cost of $15.

• C(c) = 3c; y-intercept represents the cost of each cupcake.

• C(c) = 5c + 10; y-intercept represents the total revenue.