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

Answer 1

The equation is 
b = -a
which is the same as writing
b = -1*a

The negative in front of the 'a' will flip the sign of 'a' from positive to negative, or vice versa.

Recall that,
negative times positive = negative
negative times negative = positive

Answer 2

Answer:

The direct variation says that: $y \propto x$

Then the equation is of the form:

$y=kx$ where k is the constant of Variation.

As per the statement:

A number b varies directly with the number a.

i.e $b \propto a$

By definition of direct variation:

$b = ka$              .....[1]

if $b= 2\frac{3}{4}$ and $a=-2\frac{3}{4}$

Substitute in [1] we get k;

$2\frac{3}{4}= k(- 2\frac{3}{4})$

Divide both sides by $2\frac{3}{4}$ we get;

1 = -k

or

k = -1

⇒equation becomes: b = -a

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

$b = -a$