Exploring Linear Functions: Slope and 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 + 0.10m; Slope = 0.10 (cost per mile)

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

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

If you graph the equation from the previous problem, what is the y-intercept and what does it signify in the real-world scenario?

• The y-intercept represents the maximum value of the scenario.

• The y-intercept shows the final outcome of the scenario.

• The y-intercept signifies the initial condition or starting point of the scenario being modeled.

• The y-intercept indicates the slope of the graph.

A gym charges a monthly membership fee of $50 and an additional $10 for each class attended. Write the linear equation for the total cost (C) based on the number of classes (c) attended. What does the slope represent?

• C = 10 + 50c; the slope represents the total number of classes attended.

• C = 50 + 5c; the slope represents the discount per class attended.

• C = 50c + 10; the slope represents the total cost of membership.

• C = 50 + 10c; the slope represents the cost per class attended.

Using the equation from the previous problem, if a member attends 5 classes, what will their total cost be? Graph the equation and identify the slope and y-intercept.

• $100

• $70

• $30

• $50

A delivery service charges a base fee of $15 plus $2 for each package delivered. Create a linear equation for the total cost (C) based on the number of packages (p). What does the slope indicate?

• C = 15 + 5p; the slope indicates the total cost of delivery.

• C = 10 + 3p; the slope indicates the base fee of the service.

• C = 20 + 2p; the slope indicates the number of packages delivered.

• C = 15 + 2p; the slope indicates the cost per additional package delivered.

If you were to graph the equation from the previous problem, what would the y-intercept represent?

• The y-intercept represents the value of x when y is zero.

• The y-intercept shows the slope of the line.

• The y-intercept indicates the maximum value of y.

• The y-intercept represents the value of y when x is zero.

A phone plan costs $25 per month plus $0.10 per text message sent. Write the linear equation for the total cost (C) based on the number of text messages (t). What is the slope and what does it represent?

• C = 25 + 0.05t; Slope = 0.05

• C = 25 + 0.20t; Slope = 0.20

• C = 30 + 0.10t; Slope = 0.10

• C = 25 + 0.10t; Slope = 0.10

A school is selling tickets for a play at $8 each. If they also have a fixed cost of $200 for the venue, write a linear equation for the total revenue (R) based on the number of tickets sold (n). What does the slope represent?

• R = 8n - 200; the slope represents the revenue per ticket sold.

• R = 5n - 200; the slope represents the discount per ticket.

• R = 10n - 200; the slope represents the total cost of the play.

• R = 8n + 200; the slope represents the number of tickets sold.

Using the equation from the previous problem, if the school sells 50 tickets, what will their total revenue be? Graph the equation and interpret the slope and y-intercept.

• Total revenue = 50 * p, where p is the price per ticket.

• Total revenue = 50 - p, where p is the price per ticket.

• Total revenue = 50 / p, where p is the price per ticket.

• Total revenue = 50 + p, where p is the price per ticket.