Understanding Direct Variation in Gasoline Costs

The video tutorial explains how the total cost of filling up a car with gas varies directly with the number of gallons purchased. It introduces the concept of direct variation, where the cost (y) is equal to a constant (k) times the number of gallons (x). The tutorial calculates the constant k using the cost of one gallon and demonstrates how to solve for the number of gallons that can be purchased with a given total cost. The process involves dividing the total cost by the cost per gallon and simplifying the result.

What does it mean when we say the cost of gasoline varies directly with the number of gallons?

• The cost remains constant regardless of the number of gallons.

• The cost increases as the number of gallons increases.

• The cost is unrelated to the number of gallons.

• The cost decreases as the number of gallons increases.

In the context of direct variation, what does the variable 'k' represent?

• The total cost of gasoline.

• The number of gallons purchased.

• The constant rate of variation.

• The time taken to fill the tank.

If one gallon of gasoline costs $2.25, what is the value of the constant k?

• 1.00

• 3.50

• 2.25

• 4.00

What is the equation that represents the relationship between cost and gallons in this scenario?

• y = 4.00x

• y = 2.25x

• y = 3.00x

• y = 1.50x

How many gallons can be purchased for $18 if the cost per gallon is $2.25?

• 8 gallons

• 6 gallons

• 7 gallons

• 9 gallons

What operation is used to solve for the number of gallons when given a total cost?

• Division

• Addition

• Subtraction

• Multiplication

When dividing 18 by 2.25, what is the first step in simplifying the division?

• Subtract 2.25 from 18.

• Add 18 and 2.25.

• Multiply 18 by 2.25.

• Convert 2.25 to a fraction.

What is 2.25 expressed as a fraction?

• 11/5

• 9/4

• 5/2

• 7/3

After converting 2.25 to a fraction, what is the next step in solving 18 divided by 2.25?

• Add 18 to 9/4.

• Subtract 9/4 from 18.

• Divide 18 by 4/9.

• Multiply 18 by 9/4.

What is the final result of 18 divided by 2.25?

• 8

• 9

• 7

• 6