Question 256302
Find the slope of your first line.
{{{2x-3y=6}}}
{{{-3y=-2x+6}}}
{{{y=(2/3)x-2}}}
Perpendicular lines’ slopes have the following relationship:
{{{m1*m2=-1}}}
{{{m1=(2/3)}}}
{{{m2=-(3/2)}}}
Slope-intercept form
y=mx+b
You know that {{{b=2}}}
{{{y=-(3/2)x+2}}}

{{{ graph( 300, 300, -5, 5, -5, 5, (2/3)x-2, -(3/2)x+2) }}}