Mastering Linear Functions: Slope and Intercept Insights

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) as a function of miles driven (m). What is the slope and what does it represent in this context?

• C = 50 + 0.10m; Slope = 0.10 (cost per mile)

• C = 50 + 0.20m; Slope = 0.20 (cost per mile)

• C = 50 + 0.50m; Slope = 0.50 (cost per mile)

• C = 50m; Slope = 50 (total cost per mile)

A gym charges a monthly membership fee of $30 and an additional $5 for each class attended. Write the linear equation for the total cost (C) based on the number of classes (c) attended. What is the y-intercept and what does it signify?

• C = 30 + 10c; y-intercept = 30, signifies the total cost for one class.

• C = 30 + 5c; y-intercept = 30, signifies the base membership fee.

• C = 5 + 30c; y-intercept = 5, signifies the total cost for zero classes.

• C = 30c + 5; y-intercept = 5, signifies the cost per class.

A phone plan costs $40 per month plus $0.10 for each text message sent. If you send 100 text messages in a month, what will your total bill be? Write the equation and solve for the total cost (C).

• 50

• $40

• $70

• $60

A store sells notebooks for $2 each and charges a one-time fee of $5 for a membership. Write a linear equation for the total cost (C) based on the number of notebooks (n) purchased. What does the slope represent?

• C = 2n + 5; the slope represents the cost per notebook.

• C = 3n + 5; the slope represents the discount per notebook.

• C = 2n; the slope represents the membership fee.

• C = 5n + 2; the slope represents the total cost.

A taxi charges a base fare of $3 plus $2 for every mile driven. If you drive 10 miles, what will be the total fare? Write the equation and solve for the total cost (C).

• $20

• $30

• $23

• $15

A delivery service charges a flat fee of $15 plus $1.50 per mile. Write the linear equation for the total cost (C) based on the distance (d) in miles. What does the slope indicate about the cost?

• C = 15 + 2d

• C = 15 + 1.5d

• C = 15 + 0.5d

• C = 10 + 1.5d

A concert ticket costs $25 and an additional $10 for parking. Write a linear equation for the total cost (C) based on the number of tickets (t) purchased. What is the y-intercept and what does it represent?

• C = 25t + 10; y-intercept = 10, representing the parking fee.

• C = 15t + 10; y-intercept = 10, representing the ticket price.

• C = 25t + 5; y-intercept = 5, representing a discount.

• C = 30t + 10; y-intercept = 10, representing the total cost of tickets.

A subscription service charges $12 per month plus a one-time setup fee of $20. Write the equation for the total cost (C) based on the number of months (m) subscribed. What does the slope represent in this scenario?

• C = 20m + 12; The slope represents the total cost of $20.

• C = 12m; The slope represents the setup fee of $20.

• C = 12m + 20; The slope represents the monthly cost of $12.

• C = 12m + 10; The slope represents the monthly cost of $10.

A local farmer sells apples for $3 per pound and charges a $2 fee for packaging. Write a linear equation for the total cost (C) based on the weight of apples (w) in pounds. What is the slope and what does it signify?

• C = 3w + 2; Slope = 3

• C = 3w; Slope = 0

• C = 2w + 3; Slope = 2

• C = 5w + 2; Slope = 5

A school charges $100 for a field trip plus $15 for each student attending. Write the linear equation for the total cost (C) based on the number of students (s). If 20 students attend, what is the total cost?

• 400

• 500

• 250

• 350