Exploring Slope and Intercepts in Linear Word Problems

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 in this context?

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

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

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

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

If you graph the equation from the previous problem, what is the y-intercept and what does it signify in the real-world scenario?

• The y-intercept represents the slope of the graph.

• The y-intercept indicates the rate of change in the independent variable.

• The y-intercept is the maximum value of the dependent variable.

• The y-intercept is the initial value of the dependent variable when the independent variable is zero.

A gardener charges $50 for a basic service and an additional $10 for each hour worked. Write the linear equation for the total cost (C) based on hours worked (h). What is the slope and what does it represent?

• C = 50 + 10h; Slope = 10

• C = 10 + 50h; Slope = 50

• C = 50h + 10; Slope = 50

• C = 50 + 5h; Slope = 5

Using the equation from the previous problem, graph the total cost versus hours worked. What does the slope of the line indicate about the gardener's pricing?

• The slope indicates the gardener's hourly rate.

• The slope indicates the number of hours worked.

• The slope shows the gardener's profit margin.

• The slope represents the total cost of the gardener.

A phone plan costs $30 per month plus $0.10 per text message sent. Write the linear equation for the total cost (C) based on the number of text messages (t). What is the y-intercept?

• C = 0.10 + 30t; y-intercept is 0.10.

• C = 30 + 0.05t; y-intercept is 30.

• C = 30 + 0.10t; y-intercept is 30.

• C = 30t + 0.10; y-intercept is 0.

If you were to graph the equation from the previous problem, what does the y-intercept represent in the context of the phone plan?

• The total monthly cost of the plan.

• The number of minutes included in the plan.

• The fixed cost of the phone plan.

• The cost per additional minute over the limit.

A school is selling tickets for a play. Each ticket costs $8, and there is a one-time fee of $50 for the venue. Write the linear equation for the total revenue (R) based on the number of tickets sold (n). What is the slope?

• R = 50n + 8; slope = 50

• R = 10n + 50; slope = 10

• R = 8n; slope = 0

• R = 8n + 50; slope = 8

Graph the equation from the previous problem. What does the slope tell you about the revenue generated from ticket sales?

• The slope has no effect on the revenue generated from ticket sales.

• The slope indicates a fixed revenue regardless of ticket sales.

• The slope indicates that revenue increases with each additional ticket sold.

• The slope shows that revenue decreases with each additional ticket sold.

A delivery service charges a base fee of $5 plus $2 for each package delivered. Write the linear equation for the total cost (C) based on the number of packages (p). What does the y-intercept represent?

• C = 5 + 2p; y-intercept represents the base fee of $5.

• C = 2p; y-intercept represents the total cost of delivery.

• C = 5p + 2; y-intercept represents the cost per package.

• C = 10 + 2p; y-intercept represents a discount on the base fee.

Using the equation from the previous problem, graph the total cost versus the number of packages delivered. What does the slope indicate about the delivery service's pricing structure?

• The slope represents the total revenue generated.

• The slope indicates the number of packages delivered.

• The slope shows the average delivery time per package.

• The slope indicates the cost per package delivered.