Linear Equations: Slope, Intercept & Real-World Applications

A local bakery sells cupcakes for $2 each and cookies for $3 each. If the total revenue from selling cupcakes and cookies is $120, write a standard form equation to represent this situation. What is the slope and y-intercept of the equation?

• Standard form: 3x + 2y = 120; Slope: -3/2; Y-intercept: 60

• Standard form: 2x + 3y = 120; Slope: -2/3; Y-intercept: 40

• Standard form: 2x + 5y = 120; Slope: -2/5; Y-intercept: 24

• Standard form: x + y = 120; Slope: -1; Y-intercept: 120

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a standard form equation for the total cost based on miles driven. What does the slope represent in this context?

• C = 0.20 + 50m; the slope represents the number of miles driven.

• C = 50 + 0.50m; the slope represents the total cost.

• C = 50 + 0.20m; the slope represents the cost per mile driven.

• C = 50m; the slope represents the flat fee.

A school is planning a field trip and has a budget of $500. The cost per student is $25. Write a standard form equation to represent the number of students that can attend. How would you graph this equation?

• 30x = 500

• 20x = 500

• 25x + 100 = 500

• 25x = 500

A farmer has a total of 100 animals consisting of cows and chickens. If cows are represented by x and chickens by y, write a standard form equation for this scenario. Identify the slope and intercept of the equation.

• Standard form equation: x + y = 100; Slope: -1; Y-intercept: 0

• Standard form equation: 2x + 3y = 100; Slope: 2; Y-intercept: 33.33

• Standard form equation: x - y = 100; Slope: 1; Y-intercept: 100

• Standard form equation: -x + y = 100; Slope: 1; Y-intercept: 100

A concert venue has a seating capacity of 300. If tickets are sold for $15 each, write a standard form equation to represent the total revenue based on the number of tickets sold. What is the slope of this equation?

• The slope of the equation is 15.

• The slope of the equation is 30.

• The slope of the equation is 20.

• The slope of the equation is 5.

A bookstore sells novels for $10 and textbooks for $20. If the total sales amount to $200, write a standard form equation to represent this situation. What is the y-intercept of the equation?

• 5

• 10

• 15

• 25

A taxi company charges a base fare of $3 plus $2 per mile. Write a standard form equation for the total fare based on miles traveled. What does the slope indicate in this scenario?

• F = 3 + 3m; The slope (3) indicates the total fare charged by the taxi company.

• F = 3 + 2m; The slope (2) indicates the cost per mile charged by the taxi company.

• F = 2 + 3m; The slope (3) indicates the base fare charged by the taxi company.

• F = 5 + 2m; The slope (2) indicates the distance traveled by the taxi.

A landscaping company charges a flat rate of $100 plus $15 per hour of work. Write a standard form equation for the total cost based on hours worked. How would you graph this equation?

• C = 100 + 15h

• C = 15h + 1000

• C = 100 - 15h

• C = 100h + 15