Linear Equations and Word Problems

The video tutorial covers practice problems related to linear equations, including identifying solutions on a graph, analyzing real-world scenarios like comic book purchases and fuel dispensing, and calculating costs in a sandwich purchase problem. It emphasizes understanding slopes, intercepts, and linear relationships.

Which of the following points is a solution to the equation 2x + 3y = 6?

• (0, 2)

• (0, 6)

• (2, 3)

• (3, 0)

What does the x-intercept represent in the comic book purchase scenario?

• The total number of comic books available

• The cost of one comic book

• The total money Priya has initially

• The number of comic books Priya can buy with no money left

How much does Priya spend per comic book?

• $2

• $3

• $4

• $5

If y = 1.5x, which of the following points is a solution?

• (3, 4)

• (14, 21)

• (2, 5)

• (8, 10)

In the fuel dispensing scenario, what is the slope of the line representing the fuel remaining?

• 5 gallons per second

• -5 gallons per second

• -10 gallons per second

• 10 gallons per second

How many seconds does it take to empty the fuel tank completely?

• 2000 seconds

• 1500 seconds

• 1000 seconds

• 500 seconds

What is the cost of one sandwich in the sandwich cost problem?

• $5

• $8

• $6

• $7

What is the delivery fee in the sandwich cost problem?

• $6

• $5

• $4

• $3

If 4 sandwiches cost $33 including the delivery fee, what is the cost of the sandwiches alone?

• $20

• $30

• $25

• $28

What is the equation representing the total cost of sandwiches including the delivery fee?

• y = 5x + 7

• y = 7x + 5

• y = 6x + 4

• y = 8x + 3