Mastering Slope & Intercept in Real-World Scenarios

1. A car rental company charges a flat fee of $50 plus $20 for each day the car is rented. Write the equation in standard form to represent the total cost (C) based on the number of days (d) rented. Identify the slope and y-intercept.

• C = 20d + 50

• C = 50d + 20

• 20d - C = -50

• C = 20d - 50

2. A local gym has a membership fee of $30 and charges $15 per class attended. Write the equation in standard form for the total cost (C) based on the number of classes (c) attended. What does the slope represent in this context?

• C = 30c + 15

• C = 15 + 30c

• C = 30 + 15c

• 15c + C = 30

3. A school is planning a field trip and has a budget of $500. The cost per student is $25. Write the equation in standard form to represent the number of students (s) that can attend. Identify the slope and intercept.

• 25s + 500 = 0; slope: 25, intercept: -500

• 25s - 500 = 0; slope: 25, intercept: 500

• 30s - 500 = 0; slope: 30, intercept: 500

• 20s - 500 = 0; slope: 20, intercept: 500

4. A gardener is planting flowers in a rectangular garden. The length of the garden is 3 times the width. If the total area is 300 square feet, write the equation in standard form and find the dimensions of the garden.

• Length: 30 feet, Width: 10 feet

• Length: 20 feet, Width: 15 feet

• Length: 25 feet, Width: 12 feet

• Length: 40 feet, Width: 5 feet

6. A concert venue sells tickets for $40 each and has a fixed cost of $2000 for the event. Write the equation in standard form for the total revenue (R) based on the number of tickets (t) sold. Identify the slope and intercept.

• R = 30t - 2000; Slope: 30, Intercept: -2000

• R = 40t + 2000; Slope: 40, Intercept: 2000

• R = 40t - 2000; Slope: 40, Intercept: -2000

• R = 50t - 2000; Slope: 50, Intercept: -2000

7. A factory produces widgets at a cost of $5 each and has a fixed cost of $1000. Write the equation in standard form for the total cost (C) based on the number of widgets (w) produced. What does the slope indicate?

• C = 5w - 1000; The slope (5) indicates the profit made for each widget produced.

• C = 1000w + 5; The slope (1000) indicates the fixed cost per widget produced.

• C = 10w + 1000; The slope (10) indicates the total cost for each widget produced.

• C = 5w + 1000; The slope (5) indicates the cost increase for each additional widget produced.

8. A phone plan charges a monthly fee of $30 plus $0.10 per text message sent. Write the equation in standard form for the total monthly cost (C) based on the number of text messages (m) sent. Identify the slope and intercept.

• -C + 0.10m + 30 = 0; slope = 0.10, intercept = 30

• C = 30m + 0.10; slope = 30, intercept = 0.10

• C - 0.10m - 30 = 0; slope = -0.10, intercept = -30

• C = 0.10m + 30; slope = 30, intercept = 0

9. A bookstore sells novels for $15 each and has a fixed cost of $500 for the month. Write the equation in standard form for the total revenue (R) based on the number of novels (n) sold. What does the slope represent in this scenario?

• R = 15n + 500; slope = 500

• R = 10n + 500; slope = 10

• R = 20n + 0; slope = 20

• R = 15n + 0; slope = 15

10. A taxi service charges a base fare of $3 plus $2 for each mile driven. Write the equation in standard form for the total fare (F) based on the number of miles (m) driven. Identify the slope and y-intercept.

• F = 3 + 2m; Slope: 0, Y-intercept: 3

• 2m - F = -3; Slope: 2, Y-intercept: 3

• F = 2m + 3; Slope: 2, Y-intercept: 0

• F = 3m + 2; Slope: 3, Y-intercept: 2