Exploring Intercepts: Real-World Linear Equations

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What are the x-intercept and y-intercept of this equation?

• x-intercept: (-250, 0), y-intercept: (0, 50)

• x-intercept: (0, 50), y-intercept: (250, 0)

• x-intercept: (-200, 0), y-intercept: (0, 100)

• x-intercept: (-300, 0), y-intercept: (0, 75)

Tags

CCSS.HSF-IF.C.7A

A local bakery sells cupcakes for $3 each and has a fixed cost of $30 for ingredients. Write the equation for the total revenue (R) in terms of the number of cupcakes sold (c). What do the intercepts represent in this context?

• R = 3c + 30

• R = 3c

• R = c/3

• R = 30c

Tags

CCSS.8.EE.B.5

A school is planning a fundraiser. They will earn $5 for each ticket sold and have a fixed cost of $200 for the event. Write the equation for the total profit (P) in terms of tickets sold (t). What do the intercepts indicate about the fundraiser?

• P = 10t - 200

• P = 5t + 200

• P = 5t - 200

• P = 200 - 5t

Tags

CCSS.8.EE.B.5

A delivery service charges a base fee of $15 plus $1.50 per mile. Write the equation for the total charge (C) in terms of miles driven (m). Calculate the x-intercept and y-intercept and explain their meanings.

• C = 15 + 2m; y-intercept: (0, 10); x-intercept: (-7.5, 0)

• C = 15 + 1.5m; y-intercept: (0, 15); x-intercept: (-10, 0)

• C = 15 + 2.5m; y-intercept: (0, 15); x-intercept: (-6, 0)

• C = 10 + 1.5m; y-intercept: (0, 10); x-intercept: (-6.67, 0)

Tags

CCSS.HSF-IF.C.7A

A gym membership costs $40 per month plus a one-time registration fee of $100. Write the equation for the total cost (C) in terms of months (m). What do the intercepts tell you about the cost structure?

• C = 40m - 100

• C = 100m + 40

• C = 40 + 100m

• C = 40m + 100

Tags

CCSS.HSF-IF.C.7A

A phone company offers a plan that costs $30 per month plus $0.10 per minute of calls. Write the equation for the total cost (C) in terms of minutes used (m). Find the intercepts and interpret their significance.

• C = 30 + 0.10m; y-intercept: (0, 30), x-intercept: (-300, 0)

• C = 30m + 0.10; y-intercept: (0, 0), x-intercept: (0, 300)

• C = 30 + 0.05m; y-intercept: (0, 30), x-intercept: (-600, 0)

• C = 30 + 0.20m; y-intercept: (0, 30), x-intercept: (-150, 0)

A taxi service charges a flat rate of $2.50 plus $0.50 per mile. Write the equation for the total fare (F) in terms of miles driven (m). Calculate the intercepts and explain their meanings in the context of the service.

• F = 2.50 + 0.25m; y-intercept: (0, 2.50) means total fare; x-intercept: (0, 0) means no miles driven

• F = 2.50m + 0.50; y-intercept: (0, 0) means no fare; x-intercept: (5, 0) means 5 miles free

• F = 5 + 0.50m; y-intercept: (0, 5) means base fare; x-intercept: (-10, 0) is applicable

• F = 2.50 + 0.50m; y-intercept: (0, 2.50) means base fare; x-intercept: (-5, 0) is not applicable.

Tags

CCSS.8.EE.B.5

A concert venue has a seating capacity of 500 and charges $20 per ticket. Write the equation for the total revenue (R) in terms of tickets sold (t). What do the intercepts indicate about the venue's capacity and pricing?

• R = 500t; Intercepts indicate $0 revenue at full capacity and $10,000 revenue at 0 tickets.

• R = 10t; Intercepts indicate $0 revenue at 0 tickets and $5,000 revenue at full capacity.

• R = 20t + 100; Intercepts indicate $100 revenue at 0 tickets and $10,100 revenue at full capacity.

• R = 20t; Intercepts indicate $0 revenue at 0 tickets and $10,000 revenue at full capacity.

Tags

CCSS.8.EE.B.5