Answered

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 = 2a equals negative 2 and StartFraction 3 Over 4 EndFraction. when a = –2a equals negative 2 and StartFraction 3 Over 4 EndFraction.. Which equation represents this direct variation between a and b?

b = –a
–b = –a
b – a = 0
b(–a) = 0

Answer :

ogorwyne

Option 1. The equation that represents the direct variation that exists between a and b is b = –a.

How to find the direct variation here

The direct variation is of this form y ∝ x

This gives the equation

y = kx

The constant is k

From our question we have

b ∝ a so b = ka

b = [tex]2\frac{3}{4}[/tex]

a = [tex]-2\frac{3}{4}[/tex]

Remember that b = ka

[tex]2\frac{3}{4} = -2\frac{3}{4} k[/tex]

This would cancel out to

1 = -k

or k = -1

Hence the equation would be written as

b = -a

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