coordinates

6x - 5y = 30

-5y=-6x+30

y=(6/5)x-6

the gradient of this line is   6/5

The gradient of tany perpendicular line   -5/6

Now you have

$gradient = gradient\\ \frac{-5}{6}=\frac{y--7}{x--6}$

And you can finish it.  :)