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

Answer:

$b = -a$

Step-by-step 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:

$b = -a$