In order to know whether the two lines are in perpendicular, you need to focus on their gradient.
Let m1 be the gradient of linear equation 1, y=(m1)x+c
and m2 be the gradient of liners equation 2, y=(m2)x+c
then if m1 times m2 equal to -1, then the two lines are perpendicular.
For example, if m1 is 2, then m2 need to be (-1/2) in order to form perpendicular with line 1.
So, take your question as an example.
Write both of them in the form of y=mx+c
Linear Equation 1 : y=9x-2 ; hence, m1=9
Linear Equation 2 : 6y=5-x
y=(-1/6)x+(5/6) ; hence m2=(-1/6)
Since m1*m2 is not equal to -1, [ which is 9*(-1/6)=(-3/2) ],
so, the two liners equation given are not in perpendicular.