Direct Variation and Linear Equations

The video tutorial explains the concept of direct variation, where a quantity Y varies directly as X, and how to express this relationship in equation form. It covers the calculation of the proportionality constant K and provides examples to illustrate solving direct variation problems. The tutorial also discusses the graphical representation of direct variation and extends the concept to include powers of X, emphasizing the importance of understanding the relationship between Y and X in different contexts.

What happens to Y when X increases in a direct variation?

• Y decreases

• Y becomes zero

• Y remains constant

• Y increases

What is the relationship between Y and X in direct variation?

• Y is directly proportional to X

• Y is inversely proportional to X

• Y is unrelated to X

• Y is equal to X

How is direct variation written in equation form?

• Y = X + K

• Y = X/K

• Y = KX

• Y = K + X

How do you find the proportionality constant K?

• K = X / Y

• K = Y / X

• K = Y - X

• K = Y + X

If Y = 10 when X = 30, what is the value of K?

• 10

• 3

• 1/3

• 30

Given Y varies directly as X and Y = 42 when X = 6, what is the equation?

• Y = 6X

• Y = X/6

• Y = 7X

• Y = 42X

What is the equation if Y = 9 when X = 1?

• Y = 9/X

• Y = X + 9

• Y = 9X

• Y = X/9

What is the equation if Y = 18 when X = 2?

• Y = X + 18

• Y = 9X

• Y = 18X

• Y = X/9

What is the equation if Y = 24 when X = 3?

• Y = 8X

• Y = 24X

• Y = X + 24

• Y = X/8

What is the equation if Y = 45 when X = 5?

• Y = X + 45

• Y = 9X

• Y = X/9

• Y = 45X