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

The equation would be b = -a or a = -b

I hope this helps :)

Answer 2

`b = -a`

Explanation:

Direct variation says that:

`y \propto x` then,

equation is in the form of:

`y =kx` where, k is the constant of variation.

As per the statement:

A number b varies directly with the number a.

by definition we have;

`b = ka`

Substitute b = 2 and a = -2 we have;

`2 = -2a`

Divide both sides by -2 we have;

-1 = k

or

k = -1

Then, equation we get;
`b = -a`

Therefore, equation represents this direct variation between a and b is:

`b = -a`