Question

Which equation represents a direct variation? y = 2х y=x+4 y= 1/2x y=3/x

Answer 1

Answer:option 1 and option 2 represents a direct variation.

Step-by-step explanation:

A direct variation is one in which, as one variable increases in value, the other variable increases in value. Also as one variable decreases in value, the other variable decreases in value.

Looking at the options,

1) y = 2х

When x = 2, y = 2×2 = 4

When x = 3, y = 2×3 = 6

Therefore, y = 2x is a direct variation.

2) y=x+4

When x = 2, y = 2 + 4 = 6

When x = 3, y = 3 + 4 = 7

Therefore, y = x + 4 is a direct variation.

3) y= 1/2x

When x = 2, y = 1/2×2 = 1/4 = 0.25

When x = 3, y = 1/2×3 = 1/6 = 0.17

Therefore, y = 1/2x is not a direct variation.

4) y = 3/x

When x = 2, y = 3/2 = 1.5

When x = 3, y = 3/3 = 1

Therefore, y = 3/x is not a direct variation.