Exploring Linear Equations: Slope and Intercept Insights

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

• C = 25 + 0.15m; slope = 0.15

• C = 20 + 0.15m; slope = 0.15

• C = 15 + 0.20m; slope = 0.20

Maria is saving money to buy a new bike. She currently has $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 signify?

• S = 10w + 50; y-intercept = 50, signifies initial savings.

• S = 10w + 40; y-intercept = 40, signifies savings after two weeks.

• S = 10w + 60; y-intercept = 60, signifies savings after three weeks.

• S = 5w + 50; y-intercept = 50, signifies total savings after one week.

A phone company offers a plan that costs $30 per month plus $0.10 per text message. Write a linear equation for the total cost (C) based on the number of text messages (t) sent. What does the slope represent in this context?

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

• C = 30 + 0.05t; the slope represents the number of text messages.

• C = 0.10 + 30t; the slope represents the monthly fee.

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

A gardener is planting flowers in a rectangular garden. The length of the garden is 3 feet longer than twice the width. If the width is represented by w, write a linear equation for the length (L). What is the slope of the relationship between width and length?

• L = w + 3; slope = 1

• L = 3w + 2; slope = 3

• L = 2w - 3; slope = 2

• L = 2w + 3; slope = 2

A school is selling tickets for a play. The tickets cost $5 each, and the total revenue (R) from selling t tickets can be represented by a linear equation. Write this equation and identify the slope and its meaning in this scenario.

• R = 5t; slope = 5, meaning each ticket sold adds $5 to total revenue.

• R = 3t; slope = 3, meaning each ticket sold adds $3 to total revenue.

• R = 5t + 2; slope = 5, meaning each ticket sold adds $5 to total revenue plus a fixed cost.

• R = 10t; slope = 10, meaning each ticket sold adds $10 to total revenue.

A delivery service charges a base fee of $15 plus $2 for each package delivered. Write a linear equation for the total charge (C) based on the number of packages (p). What does the y-intercept represent?

• C = 15 + 3p; The y-intercept represents the total cost of delivery.

• C = 15 + p; The y-intercept represents the number of packages delivered.

• C = 10 + 2p; The y-intercept represents the cost per package.

• C = 15 + 2p; The y-intercept represents the base fee of $15.

A local gym charges a monthly membership fee of $40 and an additional $5 for each class attended. Write a linear equation for the total cost (C) based on the number of classes (c) attended. What does the slope indicate?

• C = 20 + 5c; the slope is 5.

• C = 40 + 5c; the slope is 5.

• C = 40 + 10c; the slope is 10.

• C = 40 + 3c; the slope is 3.

A bookstore sells notebooks for $3 each. If a student buys n notebooks, write a linear equation for the total cost (C). What does the slope of this equation represent?

• C = n + 3; the slope represents the total number of notebooks.

• C = 3n; the slope represents the cost per notebook.

• C = 3n + 1; the slope represents the fixed cost of the notebooks.

• C = 5n; the slope represents the total cost of all items.

A taxi company charges a flat rate of $2.50 plus $1.50 per mile. Write a linear equation for the total fare (F) based on the number of miles (m) driven. What does the y-intercept represent in this context?

• F = 2.50m + 1.50; the y-intercept represents the total fare after one mile.

• F = 2.50 + 1.50m; the y-intercept represents the initial charge of $2.50.

• F = 2.50 + 1.00m; the y-intercept represents a discount on the initial charge.

• F = 1.50m; the y-intercept represents the cost per mile.