Exploring Slope, Intercept, and Graphing Real-Life Costs

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and y-intercept of this equation?

• C = 30 + 0.20m; Slope: 0.20, Y-intercept: 30

• C = 30 + 0.50m; Slope: 0.50, Y-intercept: 30

• C = 30 + 0.20m; Slope: 30, Y-intercept: 0

• C = 30 + 0.10m; Slope: 0.10, Y-intercept: 30

A local gym offers a membership for $50 plus $10 per class attended. Write the equation for the total cost (C) in terms of classes attended (c). Identify the slope and intercept of this equation.

• C = 50 + 15c; Slope: 15, Intercept: 50

• C = 50 + 5c; Slope: 5, Intercept: 50

• C = 40 + 10c; Slope: 10, Intercept: 40

• C = 50 + 10c; Slope: 10, Intercept: 50

Two friends are saving money for a concert. Friend A saves $15 a week, while Friend B saves $10 a week. Write the equations for the amount saved (S) over time (t) for both friends. How do the slopes compare?

• Friend A: S = 15t; Friend B: S = 10t. A saves faster (slope 15 vs 10).

• Friend A: S = 20t; Friend B: S = 5t. A saves at the same rate (slope 20 vs 5).

• Friend A: S = 15t; Friend B: S = 15t. Both save at the same rate (slope 15 vs 15).

• Friend A: S = 10t; Friend B: S = 15t. A saves slower (slope 10 vs 15).

A store sells notebooks for $2 each and pens for $1 each. If a student buys a total of 10 items for $16, write a system of equations to represent this situation. How can you graph these equations to find the solution?

• x = 8, y = 2

• x = 10, y = 0

• x = 5, y = 5

• x = 6, y = 4

A taxi charges a base fare of $3 plus $1.50 per mile. Write the equation for the total fare (F) in terms of miles (m). What does the slope represent in this context?

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

• F = 3 + 1.50m; the slope represents the cost per mile.

• F = 3 + 2m; the slope represents the total fare.

• F = 1.50 + 3m; the slope represents the base fare.

A school is planning a field trip. The cost per student is $25, and there is a fixed cost of $200 for the bus. Write the equation for the total cost (C) in terms of the number of students (s). What is the y-intercept?

• The y-intercept is 25.

• The y-intercept is 250.

• The y-intercept is 0.

• The y-intercept is 200.

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 12 items for $24, write a system of equations to represent this situation. How can you graph these equations to find the number of each item purchased?

• x + y = 12; 2x + 3y = 24

• x + y = 15; 3x + 2y = 20

• x + y = 10; 3x + 2y = 30

• x + y = 12; 3x + 2y = 24

A phone plan charges a monthly fee of $40 plus $0.10 per text message. Write the equation for the total bill (B) in terms of the number of text messages (t). Identify the slope and intercept of this equation.

• B = 40 + 0.10t; Slope: 0.10, Intercept: 40

• B = 40 + 0.20t; Slope: 0.20, Intercept: 40

• B = 30 + 0.10t; Slope: 0.10, Intercept: 30

• B = 40 + 0.05t; Slope: 0.05, Intercept: 40

A concert venue has a seating capacity of 500. If tickets are sold for $20 each and VIP tickets for $50 each, write a system of equations to represent the total revenue. How can you interpret the graph of this system to find the maximum revenue?

• The system of equations is: x + y = 500 and R = 20x + 50y.

• The system of equations is: x + y = 300 and R = 15x + 45y.

• The system of equations is: x + y = 500 and R = 25x + 40y.

• The system of equations is: x + y = 1000 and R = 10x + 30y.