Question 192461
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Given Line Eqn: 2x - 3y = -5


Via Slope-Intercept Form,{{{system(y=mx+b)}}}
{{{2x+5=3y}}} ----> {{{(2x+5)/3=cross(3)y/cross(3)}}}
{{{y=highlight((2/3))x+5/3}}}, where {{{Slope=m=2/3}}}


We're looking for the line perpendicular to this, and it's slope is the reverse reciprocal {{{m[2]=-1/m=-1/(2/3)=red(-3/2)}}}


So thru point (3,-2), via Slope-Intercept form:


{{{-2=(-3/2)(3)+b}}}
{{{-2=-9/2+b}}}
{{{b=-2+9/2=(-4+9)/2=5/2}}}, Y-Intercept (0,5/2) or (0,2.5)


It follows ---> {{{red(y=(-3/2)x+5/2)}}},---> {{{(3/2)x+y=5/2}}} ---> {{{red(3x+2y=5)}}},Answer (Std. Form)


We'll see the graph,
{{{drawing(400,400,-10,10,-10,10,graph(400,400,-10,10,-10,10,(2/3)x+5/3,(-3/2)x+5/2),blue(circle(3,-2,.15)),blue(circle(0,2.5,.12)))}}} ---> {{{red(RED=2x-3y=-5)}}}; {{{green(GREEN=3x+2y=5)}}}


Thank you,
Jojo</font>