Writing Equations & Interpreting Slope: Real-World Scenarios

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

• C = 25 + 0.15m; the slope represents the initial cost of the rental.

• C = 15 + 0.20m; the slope represents the flat fee charged.

• C = 20 + 0.10m; the slope represents the total distance driven.

• C = 20 + 0.15m; the slope (0.15) represents the cost per mile driven.

A 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?

• C = 30 + 10c; The y-intercept represents the initial cost of joining the gym.

• C = 30 + 5c; The y-intercept represents the monthly membership fee of $30.

• C = 30c + 5; The y-intercept represents the total cost of classes.

• C = 5 + 30c; The y-intercept represents the cost per class attended.

A phone plan costs $25 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 (t) sent. Interpret the slope in this scenario.

• C = 25 + 0.05t; Slope = 0.05 (cost per text message)

• C = 25 + 0.10t; Slope = 0.10 (cost per text message)

• C = 30 + 0.10t; Slope = 0.10 (cost per text message)

• C = 25 + 0.20t; Slope = 0.20 (cost per text message)

A delivery service charges a base fee of $10 and $2 for each mile driven. Write the equation for the total charge (C) based on the distance (d) in miles. What does the slope indicate about the cost?

• C = 10 + 2d; The slope indicates that the cost increases by $2 for each mile driven.

• C = 10 + d; The slope indicates that the cost increases by $1 for each mile driven.

• C = 10 + 5d; The slope indicates that the cost decreases by $5 for each mile driven.

• C = 5 + 2d; The slope indicates that the cost remains constant regardless of distance.

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

• R = 5n + 50; The y-intercept (50) represents the fixed cost of the venue.

• R = 5n + 100; The y-intercept represents the total revenue from ticket sales.

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

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

A local farmer sells apples for $2 each and has a fixed cost of $100 for supplies. Write the equation for the total revenue (R) based on the number of apples sold (a). What does the slope tell you about the revenue?

• R = 2a; The slope of 2 indicates that revenue increases by $2 for each apple sold.

• R = 2a + 100; The slope of 2 indicates that revenue increases by $2 for each apple sold but includes fixed costs.

• R = 100 - 2a; The slope of -2 indicates that revenue decreases by $2 for each apple sold.

• R = a + 100; The slope of 1 indicates that revenue increases by $1 for each apple sold.

A taxi company charges a base fare of $3 plus $2 for each mile traveled. Write the equation for the total fare (F) based on the miles traveled (m). What does the y-intercept represent in this context?

• F = 5 + 2m; The y-intercept represents a discount on the base fare.

• F = 3 + 2m; The y-intercept represents the base fare of $3.

• F = 3m + 2; The y-intercept represents the total fare for 1 mile.

• F = 2m; The y-intercept represents the cost per mile.

A subscription service charges $10 per month plus a one-time setup fee of $50. Write the equation for the total cost (C) based on the number of months (m) subscribed. Interpret the slope in this situation.

• C = 10m - 50

• C = 10m + 50

• C = 50m + 10

• C = 50 + 10m^2

A bookstore sells novels for $15 each and has a fixed cost of $200 for rent. Write the equation for the total revenue (R) based on the number of novels sold (n). What does the slope indicate about the bookstore's revenue?

• R = 200n; the slope indicates that revenue decreases by $200 for each novel sold.

• R = 10n; the slope indicates that revenue increases by $10 for each novel sold.

• R = 15n + 200; the slope indicates that revenue remains constant regardless of novels sold.

• R = 15n; the slope indicates that revenue increases by $15 for each novel sold.

A concert venue charges a flat fee of $1000 for renting the space and $5 for each ticket sold. Write the equation for the total income (I) based on the number of tickets sold (t). What does the y-intercept represent in this scenario?

• I = 1000 - 5t; The y-intercept represents the cost of renting the venue.

• I = 1000 + 10t; The y-intercept represents the total income when 10 tickets are sold.

• I = 1000 + 5t; The y-intercept (1000) represents the total income when no tickets are sold.

• I = 5t; The y-intercept represents the total number of tickets sold.