Linear Equations: Interpreting Slope and Costs in Context

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an equation to represent the total cost (C) based on the number of miles (m) driven. What is the slope and what does it represent?

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

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

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

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

A gym membership costs $30 to join and $15 per month. Write an equation for the total cost (C) after m months. What is the y-intercept and what does it represent in this context?

• C = 30 + 15m; y-intercept = 30, representing the initial joining fee.

• C = 15m; y-intercept = 15, representing the monthly fee.

• C = 30m; y-intercept = 0, representing no initial cost.

• C = 30 + 10m; y-intercept = 30, representing a discount on the joining fee.

A school is planning a field trip. The cost per student is $10, and there is a fixed cost of $200 for the bus. Write an equation for the total cost (C) based on the number of students (s). What does the slope represent?

• C = 10s + 100; the slope represents the fixed cost.

• C = 5s + 200; the slope represents the total cost.

• C = 10s + 200; the slope represents the cost per additional student.

• C = 15s + 200; the slope represents the number of students.

A gardener charges $50 for a one-time service and $20 for each additional hour worked. Write an equation for the total cost (C) based on the number of hours (h) worked. What is the y-intercept?

• $50h

• $50 + $20h

• $20

• $70

• 50

A delivery service charges a base fee of $5 plus $2 for each mile driven. If a delivery is 10 miles, what is the total cost? Write the equation and interpret the slope.

• $15

• $20

• $30

• $25

A concert ticket costs $40, and there is a service fee of $5. Write an equation for the total cost (C) based on the number of tickets (t) purchased. What does the y-intercept represent?

• C = 40t + 10; The y-intercept represents the total cost of two tickets.

• C = 45t + 5; The y-intercept represents the total cost of tickets.

• C = 40t; The y-intercept represents the cost of one ticket.

• C = 40t + 5; The y-intercept represents the service fee of $5.

A local bakery sells cupcakes for $3 each and has a fixed cost of $50 for supplies. Write an equation for the total revenue (R) based on the number of cupcakes (c) sold. What does the slope indicate?

• R = 3c; the slope indicates that each cupcake sold increases revenue by $3.

• R = 50 + 3c; the slope indicates a fixed cost of $50.

• R = 3c + 50; the slope indicates that each cupcake sold decreases revenue by $3.

• R = 3c - 50; the slope indicates that selling cupcakes incurs a loss of $3.

A taxi company charges a flat rate of $3 plus $1.50 per mile. If a customer travels 5 miles, what is the total fare? Write the equation and identify the slope.

• $8.00

• $9.50

• $10.50

• $12.00

A subscription service charges $10 per month plus a one-time setup fee of $20. Write an equation for the total cost (C) after m months. What does the y-intercept represent in this scenario?

• C = 20m + 10; The y-intercept represents the monthly fee of $10.

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

• C = 10m + 30; The y-intercept represents the total cost after three months.

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