Direct and Inverse Variation

Question 1

What is the equation for direct variation?

Answer 1

y = kx, where k is a constant (either positive or negative).

Question 2

In the case of direct variation, how do x and y vary?

Answer 2

x and y vary in the same direction; if x increases, y increases and if x decreases, y also decreases.

Question 3

What is the equation for inverse variation?

Answer 3

y = k/x, where k is a constant (only positive).

Question 4

In the case of inverse variation, how do x and y vary?

Answer 4

If x increases, y decreases and the reverse is also true.

Question 5

What are the key features of a direct variation?

Answer 5

the ratio of y to x is constant for all ordered pairs and a plot of direct variation (a straight line) must pass through the origin (as y takes a value of zero when x is zero).

Question 6

What are the key features of an inverse variation?

Answer 6

the product of y and x is a constant for all ordered pairs and a plot of inverse variation (a curve) never passes through the origin and never touches the x and y axes (as either x or y can never be zero).

Question 7

What is the formula for a direct variation relation between y and xⁿ, where n ≠ 1 and 0?

Answer 7

y = kxⁿ

Question 8

What is the formula for a direct variation relation between y and xⁿ, where n ≠ 1 and 0?

Answer 8

y = k/xⁿ

Question 9

What is the ordered pair relation for direct variation between y and xⁿ, where n ≠ 1 and 0?

Answer 9

y₁/x₁ⁿ = y₂/x₂ⁿ OR y₁/y₂ = (x₁/x₂)ⁿ

Question 10

What is the ordered pair relation for inverse variation between y and xⁿ, where n ≠ 1 and 0?

Answer 10

(y₁)(x₁ⁿ) = (y₂)(x₂ⁿ) OR y₁/y₂ = (x₂/x₁)ⁿ