Question 684046
Start with 5x-4y-6=0
5x-6 = 4y
y = {{{(5/4)x - 6/4}}}
has a slope of {{{5/4}}}
A perpendicular line will have a negative inverse/reciprocal slope of {{{-4/5}}}
...
Use the slope and the point (-2, 3) in the point-slope formula
y - 3 = {{{-4/5}}}(x--2)
y - 3 = {{{-4/5}}}(x+2)
y - 3 = {{{(-4/5)x - (4/5)(2)}}}
y - 3 = {{{(-4/5)x - 8/5}}}
y = {{{(-4/5)x - 8/5 + 3}}}
y = {{{(-4/5)x - 8/5 + 3(5/5)}}}
y = {{{(-4/5)x - 8/5 + 15/5}}}
...
{{{highlight_green(y=(-4/5)x+(7/5))}}}
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