Step 1

We find the slope of \(x-9y-5=0\) by writing it in \(y=mx+b\) form

\(x-9y-5=0\)

\(9y=x-5\)

\(y=\frac{x-5}{9}\)

\(y=\frac{1}{9}x-\frac{5}{9}\)

\(m=\frac{1}{9}\)

So, slope of the perpendicular \(=-9\)

Step 2

Given that the line is passing through (3,-1)

And we got slope \(=-9\)

So point slope form is:

\(y-(-1)=-9(x-3)\)

\(y+1=-9(x-3)\)

Step 3

Using the point slope form we find the slope intercept form

\(y-(-1)=-9(x-3)\)

\(y+1=-9(x-3)\)

\(y+1=-9x+27\)

\(y=-9x+26\)

Answer: Point slope: \(y+1=-9(x-3)\)

Slope intercept: \(y=-9x+26\)