Exploring Linear Equations: 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 equation to represent the total cost (C) in terms of miles driven (m). What is the slope and what does it represent?

• C = 15 + 0.20m; Slope = 0.20 (cost per mile)

• C = 20 + 0.15m; Slope = 0.15 (cost per mile)

• C = 20 - 0.15m; Slope = -0.15 (cost reduction per mile)

• C = 20 + 0.10m; Slope = 0.10 (cost per mile)

If a store sells notebooks for $2 each and pens for $1 each, write a linear equation to represent the total cost (C) for x notebooks and y pens. How would you interpret the slope and intercept of this equation?

• C = 2x + 1y

• C = 2x + 0y

• C = 3x + 1y

• C = 2x + 2y

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 feet longer than twice the width. Write a linear equation to represent the relationship between the length (L) and width (W). What does the slope represent in this context?

• L = 3W; The slope (3) indicates the width is three times the length.

• L = W + 3; The slope (1) represents the total length of the garden.

• L = 2W - 3; The slope (2) shows the length decreases as width increases.

• L = 2W + 3; The slope (2) represents the rate at which the length increases for each unit increase in width.

A phone plan costs $30 per month plus $0.10 per minute for calls. Write a linear equation for the total cost (C) based on the number of minutes (m) used. What does the y-intercept represent?

• C = 30 + 0.05m; The y-intercept represents the monthly fee for unlimited calls.

• C = 0.10m; The y-intercept represents the cost per minute.

• C = 30m + 0.10; The y-intercept represents the total cost after one minute.

• C = 30 + 0.10m; The y-intercept represents the base cost of the phone plan.

A taxi charges a base fare of $3 plus $2 for every mile driven. Write the linear equation for the total fare (F) in terms of miles (m). What does the slope indicate about the cost?

• F = 3 + 2m

• F = 5 + 2m

• F = 2m + 3

• F = 3m + 2

A school is selling tickets for a play. The tickets cost $5 each, and there is a $50 flat fee for the venue. Write a linear equation for the total revenue (R) based on the number of tickets sold (t). What does the y-intercept represent?

• R = 5t + 100; y-intercept represents the total revenue.

• R = 5t + 50; y-intercept represents the venue cost of $50.

• R = 10t + 50; y-intercept represents the total ticket sales.

• R = 5t; y-intercept represents the cost of each ticket.

A delivery service charges a fee of $10 plus $1.50 per package delivered. Write a linear equation for the total cost (C) based on the number of packages (p). How would you interpret the slope?

• C = 10 + 2p

• C = 5 + 1.50p

• C = 10 + 1.50p

• C = 10 + 0.50p

A gym charges a monthly membership fee of $25 plus $5 for each class attended. Write a linear equation for the total cost (C) based on the number of classes (c). What does the y-intercept represent in this scenario?

• C = 30 + 5c; y-intercept represents an additional fee.

• C = 25c + 5; y-intercept represents the cost of each class.

• C = 25 + 5c; y-intercept represents the monthly membership fee of $25.

• C = 5 + 25c; y-intercept represents the total cost for zero classes.

A concert venue has a seating capacity of 500. If tickets are sold for $20 each, write a linear equation for the total revenue (R) based on the number of tickets sold (t). What does the slope represent in this context?

• R = 10t; the slope represents the discount per ticket sold.

• R = 20 + t; the slope represents the fixed costs of the concert.

• R = 500t; the slope represents the total capacity of the venue.

• R = 20t; the slope represents the revenue per ticket sold.