Exploring Linear Equations: Slope & Intercept in Real-Life

A car rental company charges a flat fee of $30 plus $0.20 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 in this context?

• C = 30 + 0.50m; Slope = 0.50 (cost per mile)

• C = 30 + 0.20m; Slope = 0.20 (cost per mile)

• C = 30 + 0.10m; Slope = 0.10 (cost per mile)

• C = 20 + 0.20m; Slope = 0.20 (base fee)

A local gym charges a monthly membership fee of $40 and an additional $10 for each fitness class attended. Write the equation for the total cost (C) based on the number of classes (c) attended. What does the y-intercept represent?

• C = 50 + 5c; The y-intercept represents the initial sign-up fee.

• C = 40 + 10c; The y-intercept represents the monthly membership fee of $40.

• C = 40c + 10; The y-intercept represents the total cost of classes attended.

• C = 10 + 40c; The y-intercept represents the cost of each class.

A phone company offers a plan that costs $50 per month plus $0.10 for each text message sent. If you want to find the total cost (C) for sending t text messages, what is the linear equation? What does the slope indicate?

• C = 50 + 0.10t

• C = 0.10 + 50t

• C = 50 + 0.05t

• C = 50t + 0.10

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 equation for the total revenue (R) based on the number of tickets sold (n). What does the y-intercept represent?

• R = 8n; The y-intercept represents the total cost of tickets sold.

• R = 8n + 100; The y-intercept represents the cost of the venue and tickets.

• R = 8n + 50; The y-intercept represents the fixed venue fee of $50.

• R = 50n + 8; The y-intercept represents the total ticket sales.

A delivery service charges a base fee of $15 plus $2 for each mile driven. Write the equation for the total charge (C) based on the distance (d) in miles. What does the slope tell you about the cost per mile?

• C = 10 + 2d; The slope of 2 indicates the cost per mile is $1.

• C = 15 + d; The slope of 1 indicates the cost per mile is $1.50

• C = 15 + 2d; The slope of 2 indicates the cost per mile is $2.

• C = 15 + 3d; The slope of 3 indicates the cost per mile is $3.

A farmer sells apples for $3 per pound and has a fixed cost of $20 for supplies. Write a linear equation for the total revenue (R) based on the pounds of apples sold (p). What does the slope represent in this scenario?

• R = 3p + 20; the slope represents the fixed cost of supplies.

• R = 5p; the slope represents the profit per pound of apples.

• R = 3p; the slope represents the price per pound of apples.

• R = 20p; the slope represents the total cost of supplies.

A concert venue has a seating capacity of 500 and sells tickets for $25 each. If the venue sells out, what is the total revenue (R)? Write the equation for total revenue based on the number of tickets sold (t). What does the y-intercept indicate?

• R = 25t + 100; y-intercept = 100, indicating additional fees when no tickets are sold.

• R = 15t; y-intercept = 25, indicating revenue from a base ticket price.

• R = 500t; y-intercept = 500, indicating maximum revenue when all tickets are sold.

• R = 25t; y-intercept = 0, indicating $0 revenue when no tickets are sold.

A taxi company charges a flat rate of $5 plus $1.50 per mile. Write the equation for the total fare (F) based on the miles driven (m). What does the slope represent in this context?

• F = 1.50 + 5m; the slope represents the initial charge.

• F = 5 + 1.50m; the slope represents the cost per mile.

• F = 1.50m; the slope represents the distance traveled.

• F = 5 + 2m; the slope represents the total fare.

A subscription box service charges $10 per box and a one-time sign-up fee of $15. Write the equation for the total cost (C) based on the number of boxes (b) ordered. What does the y-intercept represent?

• C = 10b; The y-intercept represents the cost per box.

• C = 15b + 10; The y-intercept represents the total cost of boxes.

• C = 10b + 15; The y-intercept represents the sign-up fee of $15.

• C = 5b + 15; The y-intercept represents the discount on the first box.

A bakery sells cupcakes for $2 each and has a fixed cost of $30 for ingredients. Write the equation for the total revenue (R) based on the number of cupcakes sold (c). What does the slope indicate about the revenue per cupcake?

• R = 3c; the slope indicates the revenue per cupcake is $3.

• R = 2c; the slope indicates the revenue per cupcake is $2.

• R = 2c + 30; the slope indicates the revenue per cupcake is $1.

• R = 30 + 2c; the slope indicates the revenue per cupcake is $30.