Question 352703
Convert to slope-intercept form, {{{y=mx+b}}}
{{{2x-5y=3}}}
{{{5y=2x-3}}}
{{{y=(2/5)x-3/5}}}
Perpendicular lines have slopes that are negative reciprocals,
{{{m[1]*m[2]=-1}}}
{{{(2/5)*m{2]=-1}}}
{{{m[2]=-5/2}}}
The perpendicular line has the equation,
{{{y=-(5/2)x+b}}}
You are free to to choose any value for {{{b}}}.
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Here is the original line and three perpendicular lines for values of {{{b=0}}}, {{{b=6}}}, and {{{b=-6}}}.
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{{{graph(300,300,-10,10,-10,10,(2/5)x-3,-(5/2)x,-(5/2)x+6,-(5/2)x-6)}}}