Real-Life Applications: Intercepts and Slopes in Context

A car rental company charges a flat fee of $50 plus $20 for each day the car is rented. What are the y-intercept and slope of the cost equation, and what does each represent?

• y-intercept: 50, slope: 10

• y-intercept: 0, slope: 20

• y-intercept: 20, slope: 50

• y-intercept: 50, slope: 20

A local gym has a membership fee of $30 and charges $10 per class attended. If you graph the total cost as a function of the number of classes, what are the intercepts and what do they signify?

• The y-intercept is (0, 30) and signifies the membership fee; the x-intercept is (-3, 0) but has no practical significance.

• The y-intercept is (0, 0) and signifies no cost; the x-intercept is (3, 0) and signifies free classes after three.

• The y-intercept is (0, 10) and signifies the cost per class; the x-intercept is (0, 30) and signifies the membership fee.

• The y-intercept is (0, 40) and signifies an additional fee; the x-intercept is (-2, 0) and signifies a discount for early sign-up.

A farmer sells apples for $2 each and has a fixed cost of $100 for supplies. Write the equation for the total revenue and identify the x-intercept and y-intercept. What do these intercepts mean in this context?

• The equation for total revenue is R = 2x. The x-intercept is (0, 0) and the y-intercept is (0, 0). These intercepts indicate that if no apples are sold, the revenue is zero.

• The equation for total revenue is R = 2x + 100. The x-intercept is (0, 100) and the y-intercept is (50, 0).

• The equation for total revenue is R = 3x. The x-intercept is (0, 0) and the y-intercept is (0, 150).

• The equation for total revenue is R = 100 + 2x. The x-intercept is (50, 0) and the y-intercept is (0, 100).

A school is planning a fundraiser. They will earn $5 for each ticket sold and have a starting budget of $200. What is the slope and y-intercept of the revenue equation, and how can you interpret these values?

• Slope: 0, Y-intercept: 200

• Slope: 5, Y-intercept: 200

• Slope: 10, Y-intercept: 150

• Slope: 5, Y-intercept: 100

A delivery service charges a base fee of $15 plus $3 per mile driven. What is the equation for the total cost, and what do the slope and intercept represent in this scenario?

• C = 15 + 3m; Slope = 3 (cost per mile), Intercept = 15 (base fee)

• C = 10 + 4m; Slope = 4 (cost per mile), Intercept = 10 (base fee)

• C = 15 + 5m; Slope = 5 (cost per mile), Intercept = 15 (base fee)

• C = 20 + 2m; Slope = 2 (cost per mile), Intercept = 20 (base fee)

A phone plan costs $25 per month plus $0.10 per text message. If you graph the total cost, what are the intercepts, and how do they relate to the cost of the plan?

• Y-intercept: (0, 0); X-intercept: (0, 250) - relates to the total number of messages.

• Y-intercept: (0, 50); X-intercept: (-500, 0) - relates to a higher base cost of the plan.

• Y-intercept: (0, 25); X-intercept: (-250, 0) - relates to the base cost of the plan.

• Y-intercept: (0, 10); X-intercept: (-100, 0) - relates to the cost per message only.

A bookstore sells notebooks for $5 each and has a fixed cost of $200 for rent. Write the equation for the total cost and identify the x-intercept and y-intercept. What do these values indicate?

• Total cost equation: C = 5x + 200; y-intercept: (0, 200); x-intercept: (-40, 0) (not feasible).

• Total cost equation: C = 5x + 300; y-intercept: (0, 300); x-intercept: (-60, 0)

• Total cost equation: C = 10x + 200; y-intercept: (0, 200); x-intercept: (-20, 0)

• Total cost equation: C = 5x + 100; y-intercept: (0, 100); x-intercept: (-20, 0)

A concert venue charges a flat fee of $1000 plus $50 per ticket sold. What is the equation for total revenue, and what do the slope and intercept represent in this situation?

• R = 1000 - 50x; Slope = -50 (loss per ticket), Intercept = 1000 (fixed fee)

• R = 50x; Slope = 1000 (fixed fee), Intercept = 50 (revenue per ticket)

• R = 1000 + 100x; Slope = 100 (revenue per ticket), Intercept = 1000 (fixed fee)

• R = 1000 + 50x; Slope = 50 (revenue per ticket), Intercept = 1000 (fixed fee)

A taxi company charges a base fare of $3 plus $2 for each mile driven. What is the equation for the total fare, and how can you interpret the slope and intercept?

• F = 3 + 2m

• F = 5 + 2m

• F = 2 + 3m

• F = 3m + 2

A local bakery sells cupcakes for $3 each and has a fixed cost of $150 for ingredients. Write the equation for total sales and identify the intercepts. What do these intercepts tell you about the bakery's sales?

• Total sales equation: T(x) = 3x - 150; y-intercept: (0, -150); x-intercept: (50, 0).

• Total sales equation: T(x) = 4x - 150; y-intercept: (0, -150); x-intercept: (37.5, 0).

• Total sales equation: T(x) = 3x + 150; y-intercept: (0, 150); x-intercept: (-50, 0).

• Total sales equation: T(x) = 5x - 150; y-intercept: (0, -150); x-intercept: (30, 0).