Real-Life Linear Equations: Slope & Intercept Insights

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write the linear equation that represents the total cost (C) in terms of miles driven (m). What is the slope and what does it represent?

• C = 20 + 0.15m; slope = 0.15, representing the cost per mile.

• C = 25 + 0.15m; slope = 0.15, representing the flat fee.

• C = 15 + 0.20m; slope = 0.20, representing the base fee.

• C = 20 + 0.10m; slope = 0.10, representing the total cost.

A local gym charges a monthly membership fee of $30 and an additional $5 for each fitness class attended. Write the equation for the total cost (C) based on the number of classes (c) attended. What does the y-intercept represent in this context?

• C = 30c + 5; The y-intercept (30) represents the total cost for attending 30 classes.

• C = 5 + 30c; The y-intercept (5) represents the cost of one class attended.

• C = 30 + 10c; The y-intercept (30) represents the cost of a yearly membership fee.

• C = 30 + 5c; The y-intercept (30) represents the monthly membership fee when no classes are attended.

A school is selling tickets for a play. The tickets cost $10 each, and there is a one-time fee of $50 for the venue. Write the equation for the total revenue (R) based on the number of tickets sold (t). What does the slope indicate?

• R = 10t + 100

• R = 50t + 10

• R = 10t + 50

• R = 10t - 50

A delivery service charges a base fee of $5 plus $2 for each mile driven. Create a linear equation for the total charge (C) based on miles (m). How would you interpret the slope and y-intercept?

• C = 5m + 2

• C = 5 + m

• C = 2m

• C = 5 + 2m

A farmer sells apples for $2 per pound and has a fixed cost of $10 for packaging. Write the equation for the total revenue (R) based on pounds of apples sold (p). What does the slope represent in this scenario?

• R = 10p; the slope represents the number of pounds sold.

• R = 2p + 10; the slope represents the total revenue from all sales.

• R = 2p; the slope represents the price per pound of apples.

• R = 10 + 2p; the slope represents the total cost of apples.

A taxi company charges a base fare of $3 and $1.50 for each mile driven. Write the equation for the total fare (F) based on miles (m). What does the y-intercept signify?

• F = 3 + 1.5m; The y-intercept signifies the base fare of $3.

• F = 1.5m; The y-intercept signifies the cost per mile.

• F = 3m; The y-intercept signifies the total fare for 3 miles.

• F = 3 + 2m; The y-intercept signifies a discount on the base fare.

A subscription box service charges $25 per month plus a one-time setup fee of $15. Write the equation for the total cost (C) based on the number of months (m). What does the slope tell you about the cost?

• C = 25m; The slope (25) indicates the setup fee increase.

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

• C = 40m + 15; The slope (40) indicates the monthly cost decrease.

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

A bookstore sells notebooks for $5 each and has a fixed cost of $20 for supplies. Write the equation for the total cost (C) based on the number of notebooks (n) sold. How would you interpret the y-intercept?

• C = 5n + 20; The y-intercept (20) represents the fixed cost of supplies.

• C = 5n; The y-intercept represents the cost of one notebook.

• C = 10n + 20; The y-intercept represents the total cost of all notebooks.

• C = 5n + 10; The y-intercept represents the variable cost of supplies.

A concert venue charges $50 for a ticket and has a fixed cost of $200 for the event. Write the equation for the total revenue (R) based on the number of tickets sold (t). What does the slope represent?

• R = 50t + 200; the slope represents the total number of tickets sold.

• R = 200t; the slope represents the total cost of the event.

• R = 50t - 200; the slope represents the profit per ticket sold.

• R = 50t; the slope represents the revenue per ticket sold.

A mobile phone plan costs $30 per month plus $0.10 for each text message sent. Write the equation for the total cost (C) based on the number of text messages (x). What does the y-intercept indicate?

• C = 30 + 0.10x; The y-intercept indicates the fixed monthly cost of the plan.

• C = 30 + 0.05x; The y-intercept indicates the number of text messages sent.

• C = 30x + 0.10; The y-intercept indicates the total cost after sending messages.

• C = 0.10x; The y-intercept indicates the cost per text message.