Exploring Linear Functions and Their Real-Life Applications

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear function to represent the total cost (C) of renting a car for x miles. What is the slope of the function, and what does it represent in this context?

• The slope is 0.10, representing a discount for early return.

• The slope is 0.50, representing the total cost of the rental.

• The slope is 0.20, representing the cost per mile driven.

• The slope is 50, representing the flat fee for renting the car.

Tags

CCSS.HSF.LE.B.5

A local gym charges a monthly membership fee of $30 and an additional $5 for each fitness class attended. Write a linear function to model the total cost (C) for attending x classes in a month. How would you graph this function?

• C = 5x

• C = 30 - 5x

• C = 30 + 10x

• C = 30 + 5x

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

A delivery service charges a base fee of $15 plus $2 for each mile delivered. Write the linear function for the total cost (C) based on the distance (d) in miles. How does the graph of this function behave as the distance increases?

• C = 15 + d; the graph increases exponentially as distance increases.

• C = 10 + 3d; the graph remains constant as distance increases.

• C = 15 + 2d; the graph increases linearly as distance increases.

• C = 15 - 2d; the graph decreases linearly as distance increases.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

A phone company offers a plan that costs $40 per month plus $0.10 per text message sent. Write a linear function for the total monthly cost (C) based on the number of text messages (m) sent. What does the y-intercept represent in this scenario?

• The y-intercept represents the cost per text message sent.

• The y-intercept represents the base cost of the plan, which is $40.

• The y-intercept represents the maximum number of messages allowed in the plan.

• The y-intercept represents the total cost of sending 100 messages.

Tags

CCSS.HSF.LE.B.5

A taxi service charges a flat rate of $3 plus $1.50 for each mile driven. Write a linear function for the total fare (F) based on the distance (d) in miles. What is the significance of the slope in this context?

• F(d) = 3 + 0.5d; The slope (0.5) shows the fare decrease per mile.

• F(d) = 1.5d; The slope (1.5) indicates the total distance traveled.

• F(d) = 3 + 1.5d; The slope (1.5) indicates the fare increase per mile.

• F(d) = 3 + 2d; The slope (2) represents the total fare.

Tags

CCSS.HSF.LE.B.5

A subscription box service charges $25 per month plus $5 for each additional item included. Write a linear function to represent the total cost (C) for x additional items. How would you analyze the function's behavior as the number of items increases?

• C(x) = 20 + 5x

• C(x) = 25 + 10x

• C(x) = 30 + 5x

• C(x) = 25 + 5x

Tags

CCSS.HSF-BF.A.1A

A concert venue sells tickets for $50 each. If they sell x tickets, write a linear function to represent the total sales (S). How would you interpret the slope of this function in terms of revenue generation?

• S(x) = 100x; the slope of 100 represents the total number of tickets sold.

• S(x) = 50x; the slope of 50 represents the revenue generated per ticket sold.

• S(x) = 50 + x; the slope of 1 represents the fixed cost of the venue.

• S(x) = 50x^2; the slope of 50x represents the increasing cost per ticket sold.

Tags

CCSS.HSF.LE.B.5

A landscaping company charges a flat fee of $100 for a service plus $20 for each hour of work. Write a linear function to model the total cost (C) based on the number of hours (h) worked. How does the graph of this function change as the hours increase?

• C(h) = 100 + 20h

• C(h) = 20 + 100h

• C(h) = 80 + 25h

• C(h) = 100h + 20

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2