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].
