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 3/4when a = –2 3/4. which equation represents this direct variation between a and b?

The direct variation says that:

Then the equation is of the form:

where k is the constant of Variation.

As per the statement:

A number b varies directly with the number a.

i.e

By definition of direct variation:

             .....[1]

if and

Substitute in [1] we get k;

Divide both sides by we get;

1 = -k

or

k = -1

⇒equation becomes: b = -a

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