Mastering Linear Equations: Slope & Intercept Applications

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 is the slope and what does it represent in this context?

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

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

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

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

A gym charges a monthly membership fee of $30 and an additional $5 for each 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 = 30c + 5; The y-intercept represents the total cost for attending no classes.

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

• C = 30 + 10c; The y-intercept represents the initial fee for a premium membership.

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

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. What is the slope and what does it indicate?

• C = 25 + 0.10t; Slope = 0.10, indicating the cost per text message.

• C = 0.10 + 25t; Slope = 25, indicating the total cost.

• C = 25t + 0.10; Slope = 25, indicating the base cost.

• C = 0.10t; Slope = 0.10, indicating the cost per month.

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 (n). What does the slope represent?

• R = 50n + 10; the slope represents the total cost of the venue.

• R = 10n + 100; the slope represents the profit per ticket sold.

• R = 10n + 50; the slope represents the revenue per ticket sold.

• R = 10n; the slope represents the total number of tickets sold.

A delivery service charges a base fee of $5 plus $2 for each mile driven. Write the equation for the total charge (C) based on the distance (d) in miles. What does the y-intercept signify in this scenario?

• C = 5 + d; The y-intercept signifies the charge for zero miles driven.

• C = 5d; The y-intercept signifies the cost per mile driven without a base fee.

• C = 5 + 2d; The y-intercept signifies the base fee of $5 when no miles are driven.

• C = 2d; The y-intercept signifies the total charge for one mile driven.

A local bakery sells cupcakes for $3 each and has a fixed cost of $50 for ingredients. Write the equation for the total cost (C) based on the number of cupcakes (c) sold. What does the slope represent?

• C = 50c + 3; the slope represents the total cost.

• C = 3c + 50; the slope represents the cost per cupcake.

• C = 50 + 3c; the slope represents the number of cupcakes sold.

• C = 3c; the slope represents the fixed cost.

A taxi company charges a flat rate of $2.50 plus $1.50 per mile. Write the equation for the total fare (F) based on the distance (d) in miles. What does the y-intercept indicate?

• F = 1.50d; The y-intercept indicates the cost per mile.

• F = 2.50d + 1.50; The y-intercept indicates the total fare for 1 mile.

• F = 2.50 + 1.50; The y-intercept indicates the distance traveled.

• F = 2.50 + 1.50d; The y-intercept indicates the base fare of $2.50.

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

• C = 15m; the slope represents the total cost after one month.

• C = 10m + 25; the slope represents a discount on the monthly charge.

• C = 15m + 25; the slope represents the monthly charge of $15.

• C = 25m + 15; the slope represents the setup fee of $25.

A 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 (a) sold. What does the y-intercept represent?

• R = 2a; the y-intercept represents the total revenue when no apples are sold.

• R = 100a; the y-intercept represents the cost of supplies.

• R = 2a + 100; the y-intercept represents the total cost when no apples are sold.

• R = a; the y-intercept represents the number of apples sold.

A concert venue charges $100 for renting the space plus $10 for each ticket sold. Write the equation for the total income (I) based on the number of tickets (t) sold. What does the slope indicate about the income?

• I = 10t; The slope indicates that there is no fixed cost for renting the venue.

• I = 10 + 100t; The slope indicates that each ticket sold decreases income by $10.

• I = 100 + 10t; The slope indicates that each ticket sold increases income by $10.

• I = 100t; The slope indicates that income decreases with more tickets sold.