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?

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kenzo201 kenzo201 · Answer 1 · 2017-05-22T16:02:36+02:00

The equation would be b = -a or a = -b

I hope this helps :)

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OrethaWilkison OrethaWilkison · Answer 2 · 2019-03-07T06:58:43+01:00

Answer:

[tex]b = -a[/tex]

Step-by-step explanation:

Direct variation says that:

[tex]y \propto x[/tex] then,

equation is in the form of:

[tex]y =kx[/tex] where, k is the constant of variation.

As per the statement:

A number b varies directly with the number a.

by definition we have;

[tex]b = ka[/tex]

Substitute b = 2 and a = -2 we have;

[tex]2 = -2a[/tex]

Divide both sides by -2 we have;

-1 = k

or

k = -1

Then, equation we get; [tex]b = -a[/tex]

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

[tex]b = -a[/tex]