Question 582392
{{{8x-9y+2=0}}} --> {{{8x+2=9y}}} --> {{{8x/9+2/9=y}}} or {{{y=(8/9)x+2/9}}}
The slope of the given line is {{{8/9}}}.
A perpendicular line will have a slope of {{{-9/8}}}
Setting up an equation such as {{{-9=-7(-9/8)+b}}} and solving for b would work.
{{{-9=-7(-9/8)+b}}} --> {{{-9=63/8+b}}} --> {{{b=(-63/8)-9}}} --> {{{b=-63/8-72/8}}} --> {{{b=-135/8}}}
Otherwise, the point slope form of the equation is
{{{y-(-9))=(-9/8)(x-(-7))}}} --> {{{y+9=(-9/8)(x+7)}}} --> {{{y+9=(-9/8)x+7(-9/8)}}} --> {{{y+9=(-9/8)x-63/8}}} --> {{{y=(-9/8)x-63/8-9}}} --> {{{y=(-9/8)x-63/8-72/8}}} --> {{{y=(-9/8)x-135/8}}}
{{{graph(300,300,-16,4,-16,4,8x/9+2/9,-9x/8-135/8)}}} {{{drawing(300,300,-16,4,-16,4,
grid(1),
blue(circle(-7,-9,0.3)),
red(line(-16,-14,4,34/9)),green(line(-16,9/8,0,-135/8))
)}}}