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 = -22. Which equation
represents this direct variation between a and b?
Ob=-a
-b=-a
b-a=0
b(-a) = 0
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Answer 1

b = -a.

Explanation:

Since the problem states that "b varies directly with the number a", we can write this relationship as:

b = ka

where k is a constant of variation. Substituting b = -a, we have:

• a = ka

Solving for k, we get:

k = -1/a

Substituting this value of k in the direct variation equation, we have:

b = (-1/a) * a

Simplifying, we get:

b = -1

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

b = -1/a

Answer 2

b = -a

Explanation:

Direct variation:

y = kx

Here we have a and b, so direct variation is

b = ka

The output, b, is always the opposite (additive inverse) of a.

k = -1

b = -1 × a

b = -a

Answer: b = -a