Given:
The equation is
[tex]2x+3y=0[/tex]
To find:
Whether the equation represents a direct variation. If it does, find the constant of variation.
Solution:
The general equation of direct variation is
[tex]y=kx[/tex] ...(i)
Where, k is the constant of variation.
The equation of direct variation is always true for (0,0).
The given equation is
[tex]2x+3y=0[/tex]
It can be written as
[tex]3y=-2x[/tex]
[tex]y=-\dfrac{2}{3}x[/tex] ...(ii)
For x=0,
[tex]y=-\dfrac{2}{3}(0)[/tex]
[tex]y=0[/tex]
The given equation is true for (0,0). So, it represents a direct variation.
On comparing (i) and (ii), we get
[tex]k=-\dfrac{2}{3}[/tex]
Therefore, the constant of variation is [tex]-\dfrac{2}{3}[/tex].
