Question

Tell whether the equation represents direct variation. If it does find the

Answer 1

Given:

The equation is

$-12+8y+12=7x$

To find:

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

Solution:

If y is directly proportional to x, then

$y\propto x$

$y=kx$            ...(i)

Where, k is the constant of proportionality.

We have,

$-12+8y+12=7x$

$8y=7x$

$y=\dfrac{7}{8}x$          ...(ii)

At x=0,

$y=\dfrac{7}{8}(0)$

$y=0$

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

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

$k=\dfrac{7}{8}$

Therefore, the constant of proportionality is $k=\dfrac{7}{8}$.