Exploring Linear Functions: Slope and Intercept in Real Life

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write a linear function to represent the total cost (C) of renting a car for x miles. What is the slope and y-intercept of this function?

• Slope: 0.25, Y-intercept: 10

• Slope: 0.10, Y-intercept: 25

• Slope: 0.15, Y-intercept: 20

• Slope: 0.20, Y-intercept: 15

A gym charges a monthly membership fee of $30 and an additional $5 for each class attended. Construct a linear function to represent the total cost (C) for attending x classes. What does the slope represent in this context?

• The slope represents the number of classes attended.

• The slope represents the total monthly fee of $30.

• The slope represents the cost per class attended, which is $5.

• The slope represents the initial cost before any classes are taken.

A phone plan costs $25 per month plus $0.10 for each text message sent. Write a linear equation to model the total cost (C) based on the number of text messages (x) sent. What is the y-intercept?

• 25

• $25.10

• $0.10

• $50

A delivery service charges a base fee of $10 and $2 for each mile driven. Create a linear function to represent the total cost (C) for x miles. How would you interpret the slope in this scenario?

• C(x) = 10 + 3x; the slope (3) represents the distance traveled.

• C(x) = 10 + x; the slope (1) represents the base fee.

• C(x) = 10 + 2x; the slope (2) represents the cost per mile.

• C(x) = 10 + 5x; the slope (5) represents the total cost.

A school is selling tickets for a play at $5 each. If they sell 100 tickets, they will also receive a $200 donation. Write a linear function to represent the total money (M) raised based on the number of tickets (t) sold. What is the y-intercept?

• 200

• 500

• 0

• 100

A gardener charges a flat fee of $50 for a service plus $15 per hour worked. Write a linear equation to represent the total cost (C) for h hours of work. What does the slope indicate?

• C = 50h + 15; The slope indicates the total cost for one hour is $50.

• C = 50 + 15h; The slope indicates that for each hour worked, the total cost increases by $15.

• C = 15h; The slope indicates that the total cost remains constant regardless of hours worked.

• C = 15 + 50h; The slope indicates that for each hour worked, the total cost decreases by $15.

A local bakery sells cupcakes for $3 each and has a fixed cost of $50 for ingredients. Construct a linear function to represent the total revenue (R) from selling x cupcakes. What is the meaning of the y-intercept?

• The y-intercept is $0, representing no revenue when no cupcakes are sold.

• The y-intercept is $100, representing the total revenue from selling 33 cupcakes.

• The y-intercept is $3, representing the price of one cupcake.

• The y-intercept is $50, representing the cost of ingredients.

A taxi company charges a base fare of $2.50 and $0.50 for each mile driven. Write a linear function to represent the total fare (F) for x miles. How can you interpret the slope in this situation?

• F(x) = 2.50 + 0.50x; the slope (0.50) indicates the cost per mile.

• F(x) = 2.50 + 1.00x; the slope represents the total fare for two miles.

• F(x) = 2.50 - 0.50x; the slope indicates the discount per mile.

• F(x) = 0.50 + 2.50x; the slope shows the base fare per mile.

A concert venue charges $40 for a ticket and has a fixed cost of $500 for the event. Create a linear function to represent the total revenue (R) based on the number of tickets (t) sold. What does the y-intercept represent?

• The y-intercept represents the price of a single ticket.

• The y-intercept represents the maximum number of tickets that can be sold.

• The y-intercept represents the total revenue when no tickets are sold.

• The y-intercept represents the total cost of the event.

A subscription service charges $10 per month plus a one-time setup fee of $25. Write a linear equation to model the total cost (C) for m months. What does the slope tell you about the cost?

• C = 15m + 25; The slope (15) indicates the monthly cost decrease.

• C = 10m; The slope (10) indicates the setup fee increase.

• C = 25m + 10; The slope (25) indicates the total cost.

• C = 10m + 25; The slope (10) indicates the monthly cost increase.