Question

On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2 when a = –2. Which equation represents this direct variation between a and b?

Answer 1

y=kx is the equation for direct variation

Answer 2

The equation is b = -a

Explanation:

Given,

The number b varies directly with the number a,

That is, we can write,

b ∝ a

⇒ b = ka

Where k is the constant of proportionality,

Given, if b = 2 then a = -2,

By substituting the value,

2 = k(-2)

⇒ k = -1

Hence, the equation that represents the direct variation between a and b is,

b = -a