Slope and Intercepts: Translating Costs and Savings

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) in terms of miles driven (m). What does the y-intercept represent in this context?

• C = 50 + 0.50m; The y-intercept represents a discount on the flat fee.

• C = 50 + 0.20m; The y-intercept represents the flat fee of $50.

• C = 0.20m; The y-intercept represents the total miles driven.

• C = 50m + 0.20; The y-intercept represents the cost per mile.

A gardener is planting flowers in a straight line. The first flower is planted at 2 feet from the starting point, and each subsequent flower is planted 1.5 feet apart. Write an equation for the position of the nth flower. What does the slope represent?

• position = 2 + n * 1.5

• position = 2 + (n - 1) * 2

• position = 2 + (n - 1) * 1.5

• position = 2 + (n + 1) * 1.5

A phone plan costs $30 per month plus $0.10 per text message. If you want to find the total cost (C) based on the number of text messages (t), what is the equation? Explain the significance of the y-intercept.

• C = 30 + 0.05t

• C = 30t + 0.10

• C = 0.10 + 30t

• C = 30 + 0.10t

A factory produces 100 units of a product at a cost of $2000. For every additional unit produced, the cost increases by $15. Write an equation for the total cost (C) based on the number of units produced (x). What does the slope indicate?

• C = 15x + 500; the slope indicates the cost increase per additional unit.

• C = 10x + 1000; the slope indicates the total units produced.

• C = 20x + 2000; the slope indicates the fixed cost per unit.

• C = 15x + 2000; the slope indicates the total cost of production.

A student is saving money for a new laptop. She starts with $100 and saves $20 each week. Write an equation to represent her savings (S) after w weeks. What does the y-intercept signify?

• S = 100 + 10w; The y-intercept signifies the savings after 10 weeks.

• S = 100 + 20w; The y-intercept signifies the initial savings of $100.

• S = 100 - 20w; The y-intercept signifies the total savings after w weeks.

• S = 20w; The y-intercept signifies the amount saved each week.

A delivery service charges a base fee of $5 plus $1.50 per mile. Write an equation for the total charge (C) based on the distance (d) in miles. What does the slope represent in this scenario?

• C = 5 + 2d; the slope represents the total distance.

• C = 5 + 1.50d; the slope represents the cost per mile.

• C = 1.50d; the slope represents the delivery time.

• C = 5d + 1.50; the slope represents the base fee.

A local gym charges a membership fee of $40 plus $5 for each class attended. Write an equation for the total cost (C) based on the number of classes (c) attended. What does the y-intercept tell you?

• C = 5 + 40c; The y-intercept (5) indicates the total cost for one class.

• C = 40 + 10c; The y-intercept (40) indicates the total cost for two classes.

• C = 40 + 5c; The y-intercept (40) indicates the membership fee.

• C = 40c + 5; The y-intercept (5) indicates the cost per class.

A bike rental shop charges a one-time fee of $15 plus $2 for each hour the bike is rented. Write an equation for the total cost (C) based on the number of hours (h) rented. Explain the significance of the intercepts.

• C = 2h - 15

• C = 15h + 2

• C = 15 - 2h

• C = 15 + 2h

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 an equation for the total cost (C) based on the number of students (s). What does the slope represent?

• C = 25s; the slope represents the fixed cost.

• C = 25s + 200; the slope represents the cost per additional student.

• C = 20s + 200; the slope represents the total cost.

• C = 30s + 150; the slope represents the number of students.

A bookstore sells notebooks 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 notebooks sold (n). What does the y-intercept indicate in this context?

• R = 3n - 50; the y-intercept indicates a loss of $50 when no notebooks are sold.

• R = 3n; the y-intercept indicates that total revenue is $0 when no notebooks are sold.

• R = 50 + 3n; the y-intercept indicates the cost of supplies.

• R = 3n + 50; the y-intercept indicates total revenue is $50 when no notebooks are sold.