Mastering Linear Equations: Slope, Intercept & Word Problems

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

• Slope: 0.20, Y-intercept: 50

• Slope: 0.10, Y-intercept: 50

• Slope: 50, Y-intercept: 0.20

• Slope: 0.50, Y-intercept: 20

A gym charges a monthly membership fee of $30 plus $5 for each class attended. If you attend 4 classes in a month, how much will you pay in total? Write the equation and identify the slope and intercept.

• $50

• $70

• $60

• $40

A phone plan costs $25 per month plus $0.10 for each text message sent. Write an equation for the total cost (C) based on the number of text messages (t) sent. What does the slope represent in this context?

• C = 25t; the slope (25) represents the total monthly cost.

• C = 0.10t; the slope (0.10) represents the total cost of the plan.

• C = 25 + 0.10t; the slope (0.10) represents the cost per text message.

• C = 0.10 + 25t; the slope (25) represents the number of text messages.

A taxi charges a base fare of $3 plus $2 for every mile driven. If you want to find the total cost for a ride of x miles, write the equation. What is the y-intercept and what does it represent?

• y = 3 + 2x; y-intercept is 3, representing the base fare.

• y = 3 + 3x; y-intercept is 3, representing the cost per mile.

• y = 5 + 2x; y-intercept is 5, representing the additional fees.

• y = 2 + 3x; y-intercept is 2, representing the total cost.

Tags

CCSS.HSF.LE.B.5

A school is planning a field trip and estimates that the cost per student is $15 plus $5 for each additional student beyond 20 students. Write an equation for the total cost (C) based on the number of students (s). What is the slope?

• The slope is 10.

• The slope is 20.

• The slope is 15.

• The slope is 5.

A farmer sells apples for $3 per pound and oranges for $2 per pound. If the total revenue from selling 10 pounds of apples and 5 pounds of oranges is $45, write an equation to represent this situation. What are the slopes of the individual fruit sales?

• Equation: 4x + y = 45; Slopes: Apples = 4, Oranges = 1

• Equation: 3x + 3y = 45; Slopes: Apples = 3, Oranges = 3

• Equation: 3x + 2y = 45; Slopes: Apples = 3, Oranges = 2

• Equation: 2x + 3y = 45; Slopes: Apples = 2, Oranges = 3

Tags

CCSS.8.EE.C.8C

A concert ticket costs $50, and there is an additional service fee of $10. Write an equation for the total cost (C) of buying x tickets. Identify the slope and y-intercept of this equation.

• C = 50x + 5; Slope: 50, Y-intercept: 5

• C = 60x + 10; Slope: 60, Y-intercept: 10

• C = 50x + 10; Slope: 50, Y-intercept: 10

• C = 50x + 15; Slope: 50, Y-intercept: 15

A local bakery sells cupcakes for $2 each and cookies for $1 each. If you buy a total of 12 items for $20, write a system of equations to represent this situation. What do the slopes of the equations indicate?

• x + y = 12; 2x + y = 20

• x + 2y = 12; x + y = 20

• 3x + y = 12; 2x + 3y = 20

• x + y = 10; 2x + y = 18

Tags

CCSS.8.EE.C.8C

A subscription service charges $10 per month plus $2 for each movie rented. Write an equation for the total cost (C) based on the number of movies (m) rented. What does the slope represent in this scenario?

• C = 10m + 2; the slope represents the total cost.

• C = 2m; the slope represents the number of movies rented.

• C = 10 + 2m; the slope represents the cost per movie rented.

• C = 2 + 10m; the slope represents the monthly fee.