Question 329565
You mean m=1/3?
{{{y=(1/3)x+b}}}
USe (-1,2) to solve for b
{{{2=(1/3)(1)+b}}}
{{{b=5/3}}}
{{{highlight( y=(1/3)x+7/3) }}}
{{{drawing(300,300,-5,5,-5,5,circle(-1,2,.2),grid(1),graph(300,300,-5,5,-5,5,0,(1/3)x+7/3))}}}
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Parallel lines have identical slopes.
{{{y=(1/2)x+b}}}
{{{3=(1/2)(1)+b}}}
{{{b=5/2}}}
{{{highlight(y=(1/2)x+5/2)}}}
{{{drawing(300,300,-5,5,-5,5,circle(1,3,.2),grid(1),graph(300,300,-5,5,-5,5,(1/2)x-2,(1/2)x+5/2))}}}
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Perpendicular lines have slopes that are negative reciprocals,
{{{m1*m2=-1}}}
{{{3*m2=-1}}}
{{{m2=-1/3}}}
{{{y=-(1/3)x+b}}}
{{{2=-(1/3)(-2)+b}}}
{{{b=4/3}}}
{{{highlight(y=-(1/3)x+8/3)}}}
{{{drawing(300,300,-5,5,-5,5,circle(-2,2,.2),grid(1),graph(300,300,-5,5,-5,5,3x+2,-(1/3)x+4/3))}}}