Question

write the equation of the line perpendicular to 9x-5y that passes through the point (2,-5) in slope-intercept form and in standard form

Answer 1

It can be easiest to start with something that looks almost like standard form.
.. 5(x -2) +9(y +5) = 0 . . . . . swap coefficients and negate one
.. 5x +9y = -35 . . . . . . . . standard form

Now, solve for y
.. y = (-5x -35)/9
.. y = (-5/9)x -35/9 . . . . . slope-intercept form