Understanding Slope and Intercept in Linear Functions

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

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

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

• C = 50 + 0.20m; Slope = 1.00 (cost per mile)

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

A gardener is planting flowers in a straight line. If he plants 5 flowers every hour, write a linear function to represent the number of flowers (F) planted after h hours. What is the rate of change?

• F(h) = 5h; Rate of change = 5

• F(h) = 5h + 2; Rate of change = 5

• F(h) = 3h; Rate of change = 3

• F(h) = 10h; Rate of change = 10

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

• C = 30 + 0.05t; The y-intercept represents the number of text messages sent.

• C = 30 + 0.10t; The y-intercept represents the fixed monthly cost of the phone plan.

• C = 30t + 0.10; The y-intercept represents the total cost of all text messages.

• C = 0.10 + 30t; The y-intercept represents the cost per text message.

A store sells notebooks for $2 each. If the total cost (C) for buying n notebooks is represented by a linear function, what is the slope of this function?

• 1

• 5

• 2

• 3

A train travels at a constant speed of 60 miles per hour. Write a linear equation that represents the distance (d) traveled after t hours. What does the slope represent in this scenario?

• d = 60t + 10; the slope represents the total distance traveled after 10 hours.

• d = 60t; the slope represents the speed of the train (60 miles per hour).

• d = 60t^2; the slope represents the acceleration of the train.

• d = 30t; the slope represents the average speed of the train (30 miles per hour).

A subscription service charges $15 per month. If you want to find the total cost (C) after m months, what is the linear equation? What does the y-intercept indicate?

• C = 15m + 5; the y-intercept indicates the initial cost is $5.

• C = 15m; the y-intercept indicates the initial cost is $0.

• C = 10m; the y-intercept indicates the initial cost is $10.

• C = 20m; the y-intercept indicates the initial cost is $5.

A factory produces 100 toys in the first hour and increases production by 20 toys every hour. Write a linear function for the total number of toys (T) produced after h hours. What is the rate of change?

• T(h) = 80h + 20; Rate of change = 80

• T(h) = 20h + 100; Rate of change = 10

• T(h) = 100h; Rate of change = 100

• T(h) = 20h + 80; Rate of change = 20

A student scores 80 points on a test and increases her score by 5 points for each additional study hour. Write the equation for her score (S) based on hours studied (h). What does the slope represent?

• S = 80 + 5h; the slope represents the score increase per hour studied.

• S = 85 + 5h; the slope represents the initial score.

• S = 80 + 10h; the slope represents the score decrease per hour studied.

• S = 80 - 5h; the slope represents the total score.

A bike rental shop charges a one-time fee of $10 plus $5 for each hour rented. Write the equation for the total cost (C) in terms of hours (h). What does the y-intercept signify?

• C = 10 + 5h; The y-intercept signifies the initial fee of $10.

• C = 10 + 2h; The y-intercept signifies a discount on the initial fee.

• C = 10h; The y-intercept signifies the total cost after 10 hours.

• C = 5h; The y-intercept signifies the cost per hour.

A delivery service charges $25 for the first 5 miles and $3 for each additional mile. Write the piecewise function for the total cost (C) based on the distance (d) in miles. What is the rate of change after the first 5 miles?

• $10 flat fee

• $3 per mile

• $5 per mile

• $2 per mile