Direct Variation and Proportionality Concepts

This video tutorial introduces the concept of direct variation, providing definitions and real-life examples such as hourly wages and spring stretching. It explains the mathematical representation of direct variation, including the constant of proportionality, and demonstrates how to solve related problems. The video also covers Hook's Law as an application of direct variation and explores variations involving squared variables.

Which of the following is an example of direct variation?

• The distance traveled and the fuel efficiency of a car

• The temperature and the amount of ice cream sold

• The number of hours worked and the total pay received

• The number of books read and the number of pages in each book

What is the constant of proportionality in the equation Y = KX?

• K

• None of the above

• X

• Y

Which of the following statements is true for direct variation?

• Y decreases as X increases

• Y is inversely proportional to X

• Y increases as X increases

• Y is constant regardless of X

In the context of direct variation, what does a graph of Y = KX look like?

• A vertical line

• A horizontal line

• A curve

• A straight line through the origin

In a direct variation, if Y = 54 when X = 9, what is the value of K?

• 6

• 54

• 9

• None of the above

According to Hook's Law, what does the displacement of a spring vary directly with?

• The color of the spring

• The length of the spring

• The mass of the object

• The temperature of the environment

If a spring stretches 10 cm with a 3 kg mass, what is the displacement with a 5 kg mass?

• 16 and 2/3 cm

• 30 cm

• 20 cm

• 25 cm

In a variation where Y varies directly with the square of X, what is the equation form?

• Y = KX

• Y = KX^2

• Y = K/X

• Y = K/X^2

If Y = 32 when X = 4 in a direct variation with the square of X, what is the value of K?

• 4

• 2

• 8

• 1

What is the value of Y when X = 6 in the equation Y = 2X^2?

• 72

• 48

• 36

• 96