Question 321919
Parallel lines have identical slopes.
{{{y=3x+b}}}
Use the point (2,-4) to solve for {{{b}}}.
{{{-4=3(2)+b}}}
{{{b+6=-4}}}
{{{b=-10}}}
{{{highlight(y=3x-10)}}}
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Perpendicular lines have slopes that are negative reciprocals,
{{{m1*m2=-1}}}
{{{3*m2=-1}}}
{{{m2=-1/3}}}
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{{{y=-(1/3)x+b}}}
Again, use the point (2,-4) to solve for b,
{{{-4=-2/3+b}}}
{{{b=-12/3+2/3}}}
{{{b=-10/3}}}
{{{highlight(y=-(1/3)x-10/3)}}}
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{{{drawing(300,300,-6,6,-6,6,grid(1),circle(2,-4,.3),graph(300,300,-6,6,-6,6,3x-10,-(1/3)x-10/3,3x-2))}}}
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Blue line is the original line.
Red line is the parallel line.
Green line is the perpendicular line.