Question 128875
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Discussion
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The equation of a line passing through two points is given by {{{y-y[1]=((y[1]-y[2])/(x[1]-x[2]))(x-x[2])}}}.
You need to derive the equations for both of your
lines and then put them into slope-intercept form {{{y=mx+b}}}, so that you can
compare the slope numbers for the two lines.


Lines are parallel if and only if their slopes are equal, i.e. {{{m[1]=m[2]}}}.


Lines are perpendicular if and only if their slopes are negative reciprocals,
i.e. {{{m[1]=-1/m[2]}}} 
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Solution
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Line 1:
{{{y-(-2)=(((-2)-(-4))/(1-(-2)))(x-(-2))}}}
{{{y+2=(2/3)(x+2)}}}
{{{y+2=2x/3+4/3}}}
{{{y=2x/3-2/3}}}

Line 2:
{{{y-2=((2-5)/(2-0))(x-2)}}}
{{{y-2=(-3/2)(x-2)}}}
{{{y-2=-3x/2+3}}}
{{{y=-3x/2+5}}}


The slope of Line 1 is {{{2/3}}}.  The negative reciprocal of {{{2/3}}} is {{{-3/2}}} which is the slope of Line 2.

Therefore the lines are perpendicular.


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Check Answer
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They look perpendicular to me:


{{{drawing(400,400,-5,5,-5,5,
grid(1),
graph(400,400,-5,5,-5,5,2x/3-2/3,-3x/2+5)
)}}}
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