Linear Functions and Graphing in Real-Life Scenarios

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

• 0.50

• 0.20

• 1.00

• 0.10

If you graph the linear function from the previous question, what does the y-intercept represent in this real-world scenario?

• The final outcome of the scenario.

• The slope of the line in the graph.

• The rate of change in the scenario.

• The initial value or starting point of the scenario.

A gym charges a monthly membership fee of $30 plus $5 for each class attended. Write the equation for the total cost (C) based on the number of classes (c) attended. How would you graph this equation?

• C = 30 - 5c

• C = 30 + 5c

• C = 5c

• C = 30 + 10c

If a student studies for 2 hours and scores 80% on a test, and studies for 4 hours and scores 90%, can you identify a linear function that models the relationship between hours studied (h) and test score (s)? What is the equation?

• s = 4h + 80

• s = 10h + 50

• s = 5h + 70

• s = 2h + 75

A store sells notebooks for $2 each and pens for $1 each. If a student buys a total of 10 items for $16, write a system of linear equations to represent this situation. How would you graph these equations?

• x + y = 10; 2x + y = 16

• x + y = 8; 2x + y = 18

• x + y = 12; 2x + y = 14

• x + y = 10; 3x + y = 16

A taxi charges a base fare of $3 plus $2 for every mile driven. If you were to graph the cost (C) against the distance (d), what would the slope and y-intercept represent?

• The slope represents the base fare, and the y-intercept represents the cost per mile.

• The slope represents the distance per mile, and the y-intercept represents the total fare.

• The slope represents the cost per mile, and the y-intercept represents the base fare.

• The slope represents the total cost, and the y-intercept represents the distance traveled.

A farmer sells apples for $1.50 per pound. If he sells 10 pounds, how much money does he make? Write a linear function to represent the total earnings (E) based on pounds sold (p).

• $15

• $20

• $10

• $5

If the linear function from the previous question is graphed, what does the slope indicate about the relationship between pounds sold and earnings?

• The slope indicates a negative relationship between pounds sold and earnings.

• The slope indicates a positive relationship between pounds sold and earnings.

• The slope indicates a constant relationship regardless of pounds sold.

• The slope has no effect on the relationship between pounds sold and earnings.

A local bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 12 items for $24, write a linear equation to represent this situation. How would you graph it?

• x + y = 12; 3x + 2y = 24

• x + y = 12; 2x + 3y = 24

• x + y = 10; 3x + 2y = 20

• x + y = 15; 3x + 2y = 30

A phone plan costs $40 per month plus $0.10 per text message. Write a linear function to represent the total cost (C) based on the number of text messages (t) sent. What does the slope of this function indicate?

• C(t) = 40 + 0.10t; the slope (0.10) indicates the cost per text message.

• C(t) = 40 + 0.05t; the slope (0.05) indicates the cost per text message.

• C(t) = 0.10 + 40t; the slope (40) indicates the number of text messages.

• C(t) = 40t; the slope (40) indicates the total monthly cost.