Algebra: Writing Equations & Interpreting Slope/Intercept

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?

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

• C = 15 + 0.15m; Slope = 0.15, representing the base charge.

• C = 20 + 0.20m; Slope = 0.20, representing the flat fee.

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

A gym membership costs $30 to join and $25 per month. Write the equation for the total cost (C) after m months. What does the y-intercept represent in this context?

• C = 30m + 25; The y-intercept represents the total cost after one month.

• C = 30 + 25m; The y-intercept represents the initial joining fee of $30.

• C = 25m; The y-intercept represents the monthly fee of $25.

• C = 30 + 30m; The y-intercept represents the cost of joining and the first month combined.

A phone plan charges a base fee of $50 and an additional $0.10 for each text message sent. Write the equation for the total cost (C) based on the number of text messages (t). What does the slope indicate?

• C = 50 + 0.05t; the slope indicates the total number of messages.

• C = 50 + 0.20t; the slope indicates the base fee.

• C = 50 + 0.10t; the slope indicates the cost per text message.

• C = 50t; the slope indicates the total cost without messages.

A local bakery sells cupcakes for $3 each and charges a $5 box fee. Write the equation for the total cost (C) of buying x cupcakes. What does the y-intercept represent?

• C = 3x + 5; The y-intercept represents the box fee of $5.

• C = 3x + 10; The y-intercept represents the total cost of two boxes.

• C = 5x + 3; The y-intercept represents the total cost of cupcakes without the box fee.

• C = 3x; The y-intercept represents the cost of one cupcake.

A student is saving money for college. They start with $200 and save $50 each month. Write the equation for the total savings (S) after m months. What does the slope tell you about their savings?

• S = 200 + 50m

• S = 50m

• S = 200 + 25m

• S = 200 - 50m

A taxi company charges a $2.50 base fare and $0.75 per mile. Write the equation for the total fare (F) based on miles driven (m). What does the y-intercept represent in this scenario?

• F = 2.50 + 0.50m; The y-intercept represents the discount on the fare.

• F = 2.50m + 0.75; The y-intercept represents the total fare for one mile.

• F = 2.50 + 0.75m; The y-intercept (2.50) represents the base fare.

• F = 0.75m; The y-intercept represents the cost per mile.

A concert ticket costs $45 and there is a service fee of $5. Write the equation for the total cost (C) of buying t tickets. What does the slope represent?

• C = 45t; The slope represents the service fee per ticket.

• C = 50t + 5; The slope represents the total cost of all tickets.

• C = 45t + 5; The slope represents the cost of each additional ticket.

• C = 40t + 10; The slope represents the discount on each ticket.

A bookstore sells novels for $12 each and has a membership fee of $10. Write the equation for the total cost (C) of buying n novels. What does the y-intercept indicate?

• C = 12n; y-intercept indicates the cost of one novel.

• C = 10 + 12n; y-intercept indicates the membership fee of $10.

• C = 10n; y-intercept indicates the total cost of n novels.

• C = 10 + 5n; y-intercept indicates a discount on membership.

A landscaping service charges a flat fee of $100 plus $50 per hour of work. Write the equation for the total cost (C) based on hours worked (h). What does the slope represent?

• C = 100 + 50h; the slope represents the cost per hour of work.

• C = 50h; the slope represents the hourly rate without a base fee.

• C = 50 + 100h; the slope represents the initial fee.

• C = 100h; the slope represents the total cost.

A subscription service charges $15 per month with a one-time sign-up fee of $10. Write the equation for the total cost (C) after m months. What does the y-intercept represent in this case?

• C = 10m + 15; The y-intercept represents the monthly fee of $15.

• C = 15m; The y-intercept represents the total cost after one month.

• C = 10m + 15; The y-intercept represents the total cost after two months.

• C = 15m + 10; The y-intercept represents the one-time sign-up fee of $10.