Question

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

constant of direct variation. -12 + 8y +12 = 7x.

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=(7)/(8)x` ...(ii)

At x=0,

`y=(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=(7)/(8)`

Therefore, the constant of proportionality is
`k=(7)/(8)`.