Exploring Linear Equations: Slope and Intercept in 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 = 15 + 0.15m; Slope = 0.15 (base fee)

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

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

• C = 20 + 0.10m; Slope = 0.10 (cost per mile)

If you have $50 and you spend $5 each week, write an equation to represent the amount of money (M) you have left after w weeks. How many weeks will it take for you to have $20 left?

• 4 weeks

• 8 weeks

• 6 weeks

• 10 weeks

A store sells notebooks for $2 each and pens for $1 each. If you buy a total of 10 items and spend $16, write a system of equations to represent this situation. What is the slope of the line representing the cost of notebooks?

• 1

• -2

• -1

• 0

A gardener is planting flowers in rows. If each row contains 5 flowers and the total number of flowers planted is represented by the equation F = 5r, where r is the number of rows, what does the slope represent in this context?

• The slope represents the height of the flowers.

• The slope represents the number of flowers per row, which is 5.

• The slope represents the total number of flowers planted.

• The slope represents the number of rows of flowers.

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

• F = 5 + 2m; the y-intercept represents the minimum fare.

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

• F = 3m + 2; the y-intercept represents the cost per mile.

• F = 2m; the y-intercept represents the total fare.

You are saving money for a video game that costs $60. If you save $10 each week, write an equation to represent your savings (S) after w weeks. How many weeks will it take to save enough money?

• 6 weeks

• 10 weeks

• 8 weeks

• 4 weeks

A phone plan costs $30 per month plus $0.10 per text message. Write a linear equation for the total cost (C) in terms of the number of text messages (t). What does the slope indicate?

• C = 30t + 0.10; the slope indicates the total cost.

• C = 30 + 0.05t; the slope indicates the discount per text message.

• C = 30 + 0.20t; the slope indicates the monthly fee.

• C = 30 + 0.10t; the slope (0.10) indicates the cost per text message.

A factory produces 100 toys per hour. If the production rate increases by 20 toys per hour, write an equation to represent the total number of toys (T) produced after h hours. What does the slope of this equation represent?

• T = 140h; the slope represents the total production after 2 hours.

• T = 120h; the slope represents the production rate of 120 toys per hour.

• T = 100h; the slope represents the initial production rate of 100 toys per hour.

• T = 120h; the slope represents the increase in production rate over time.

A school is planning a field trip and charges $15 per student. If there are 30 students, write an equation to represent the total cost (C) for the trip. What does the y-intercept represent in this scenario?

• C = 15n + 5; y-intercept represents $5.

• C = 30n; y-intercept represents $15.

• C = 15n; y-intercept represents $0.

• C = 15 + n; y-intercept represents total students.

A bike rental shop charges a one-time fee of $10 plus $5 for each hour rented. Write the equation for the total cost (C) in terms of hours (h). How much would it cost to rent a bike for 4 hours?

• $20

• $30

• $25

• $35