Analyzing Slope & Intercept in Grade 8 Word Problems

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and what does it represent in this context?

• C = 30 + 0.50m; Slope = 0.50 (cost per mile)

• C = 30 + 0.10m; Slope = 0.10 (cost per mile)

• C = 30 + 0.20m; Slope = 30 (fixed cost)

• C = 30 + 0.20m; Slope = 0.20 (cost per mile)

A local gym offers a membership for $50 plus $10 per class attended. If you graph the total cost (C) against the number of classes (c), what does the y-intercept represent?

• The initial membership fee of $50.

• The maximum number of classes allowed per month.

• The total cost after attending one class.

• The cost of each individual class attended.

Two friends are selling lemonade. Friend A sells it for $2 per cup, while Friend B sells it for $1.50 per cup. Write the equations for their total earnings (E) based on the number of cups sold (x). How can you find the point where their earnings are equal?

• The point where their earnings are equal is at x = 10.

• The point where their earnings are equal is at x = 5.

• The point where their earnings are equal is at x = 0.

• The point where their earnings are equal is at x = 2.

A school is planning a field trip. The cost per student is $15, and there is a fixed cost of $200 for the bus. Write the equation for the total cost (C) in terms of the number of students (s). What does the slope represent?

• C = 15s - 200; the slope represents the total cost.

• C = 15s + 100; the slope represents the cost per student.

• C = 15s + 200; the slope represents the cost per additional student.

• C = 200s + 15; the slope represents the fixed cost.

A farmer has two types of crops. Crop A yields $300 per acre, and Crop B yields $200 per acre. If the farmer has 10 acres to plant, write the equations for the total revenue (R) from each crop. How can you determine the feasible solutions for planting both crops?

• R = 200x + 300y; constraint: x + y <= 5, x >= 0, y >= 0.

• R = 300x + 200y; constraint: x + y = 10, x >= 0, y >= 0.

• R = 300x + 200y; constraint: x + y <= 10, x >= 0, y >= 0.

• R = 300x + 200y; constraint: x + y >= 10, x >= 0, y >= 0.

A bookstore sells novels for $12 each and textbooks for $20 each. If a student has $120 to spend, write the equations for the total number of novels (n) and textbooks (t) they can buy. What does the intercept represent in this scenario?

• The equations are 15n + 20t = 120. The intercepts represent the price of novels and textbooks.

• The equations are 10n + 15t = 120. The intercepts represent the total cost of novels and textbooks.

• The equations are 12n + 25t = 120. The intercepts represent the number of novels and textbooks bought together.

• The equations are 12n + 20t = 120. The intercepts represent the maximum number of novels (10) and textbooks (6) the student can buy.

A concert venue has a seating capacity of 500. If tickets are sold for $25 each, write the equation for total revenue (R) in terms of the number of tickets sold (t). How can you interpret the slope in this context?

• R = 500t

• R = 25 + t

• R = 25t

• R = 25t + 100

A charity event has a goal of raising $1,000. If each ticket sold is $20, write the equation for the total amount raised (R) in terms of the number of tickets sold (t). What does the slope indicate about the fundraising effort?

• R = 20t; the slope indicates that each ticket sold raises $20.

• R = 10t; the slope indicates that each ticket sold raises $10.

• R = 1000t; the slope indicates that each ticket sold raises $1000.

• R = 20t + 100; the slope indicates that each ticket sold raises $20 plus a fixed amount.

A company produces two products. Product X costs $5 to make and Product Y costs $8. If the company has a budget of $200, write the equations for the total cost (C) based on the number of products made (x and y). How can you find the feasible solutions for production?

• C = 5x + 8y; 5x + 8y = 200

• C = 5x + 5y; 5x + 5y <= 200

• C = 8x + 5y; 8x + 5y <= 200

• C = 5x + 8y; 5x + 8y <= 200