Answered

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Tell whether the equation represents direct variation. If it does find the
constant of direct variation. -12 + 8y +12 = 7x.

Sagot :

Given:

The equation is

[tex]-12+8y+12=7x[/tex]

To find:

The constant of direct variation if the given equation represents direct variation.

Solution:

If y is directly proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]            ...(i)

Where, k is the constant of proportionality.

We have,

[tex]-12+8y+12=7x[/tex]

[tex]8y=7x[/tex]

[tex]y=\dfrac{7}{8}x[/tex]          ...(ii)

At x=0,

[tex]y=\dfrac{7}{8}(0)[/tex]

[tex]y=0[/tex]

The equation (ii) passes through (0,0). So, it represents a proportional relationship.

On comparing (i) and (ii), we get

[tex]k=\dfrac{7}{8}[/tex]

Therefore, the constant of proportionality is [tex]k=\dfrac{7}{8}[/tex].

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