Exploring Linear Equations: Slope & 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 = 20 + 0.10m; Slope = 0.10 (cost per mile)

• C = 20 + 0.20m; Slope = 0.20 (cost per mile)

• C = 15 + 0.15m; Slope = 0.15 (base fee)

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

Maria is saving money to buy a new bike. She starts with $50 and saves $10 each week. Write a linear equation to represent her savings (S) after w weeks. What is the y-intercept and what does it represent?

• S = 10w + 60; y-intercept = 60 (savings after 1 week)

• S = 10w + 50; y-intercept = 50 (initial savings)

• S = 5w + 50; y-intercept = 50 (initial savings)

• S = 10w + 40; y-intercept = 40 (total savings after 4 weeks)

A phone company charges a monthly fee of $30 plus $5 for each gigabyte of data used. Write a linear equation for the total bill (B) based on data usage (d). What does the slope represent in this context?

• B = 30d + 5; the slope represents the total monthly fee.

• B = 5d; the slope represents the total data used.

• B = 5 + 30d; the slope represents the fixed cost of the plan.

• B = 30 + 5d; the slope represents the cost per gigabyte of data.

A gardener is planting flowers in rows. Each row can hold 8 flowers. If the gardener plants x rows, write a linear equation for the total number of flowers (F) planted. What is the slope and what does it indicate?

• F = 10x; slope = 10

• F = 6x; slope = 6

• F = 8x; slope = 8

• F = 4x; slope = 4

A school is selling tickets for a play. Each ticket costs $12. Write a linear equation to represent the total revenue (R) from selling t tickets. What does the slope represent in this scenario?

• R = 10t; the slope represents the fixed cost of the play.

• R = 12t; the slope represents the revenue per ticket sold.

• R = 12t - 12; the slope represents the discount applied to each ticket.

• R = 12t + 5; the slope represents the total number of tickets sold.

Tom is collecting baseball cards. He has 15 cards and plans to buy 3 more each month. Write a linear equation for the total number of cards (C) he will have after m months. What is the y-intercept and what does it signify?

• C = 15 + 3m; y-intercept = 15

• C = 15 + 5m; y-intercept = 5

• C = 15 + 2m; y-intercept = 2

• C = 12 + 3m; y-intercept = 12

A factory produces 200 toys per day. If the production increases by 50 toys each day, write a linear equation for the total number of toys (T) produced after d days. What does the slope represent?

• T = 200 + 50d

• T = 150 + 50d

• T = 50d + 200

• T = 200d + 50

A bookstore sells notebooks for $5 each. If they sell n notebooks, write a linear equation for the total sales (S). What is the slope and what does it indicate about the sales?

• S = 5n; slope = 5

• S = n; slope = 1

• S = 10n; slope = 10

• S = 5n + 2; slope = 5

A train travels at a speed of 60 miles per hour. Write a linear equation for the distance (D) traveled after t hours. What does the slope represent in this situation?

• D = 60t^2; the slope represents the acceleration of the train.

• D = 30t; the slope represents the total distance traveled.

• D = 60t; the slope represents the speed of the train.

• D = 60t + 10; the slope represents the time taken.

A restaurant's daily sales can be modeled by the equation S = 200 + 15d, where d is the number of days since opening. What does the y-intercept represent in this context?

• The y-intercept shows the maximum sales the restaurant can achieve.

• The y-intercept represents the average daily sales over the first month.

• The y-intercept indicates the total sales after one week.

• The y-intercept represents the initial sales amount on the day the restaurant opened.