```Question 73812
First find the slope of the line connecting the two points (3, 12) and (5, 4).
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Recall that the slope is defined as the change in y values divided by the change in x values.
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In going from point (3,12) to point (5,4) note that the value of x goes from +3 to +5, a
change of +2.  Also in going from point (3,12) to point (5,4) note that y goes from +12
to +4, a change of -8.
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Therefore, the slope, call it m, of this line is:
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{{{m = (-8)/(2)= -4}}}
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Once you have the slope of the line, you take the negative inverse of the slope and you have
the slope of the perpendicular line.
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The inverse of -4 is {{{1/-4}}} and the negative of that is {{{-1/-4 = 1/4}}}
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So answer D is the correct answer.  The slope of the line perpendicular to the line that
joins the points (3,12) and (5,4) is {{{1/4}}}.
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Hope this helps.  To find the slope of a perpendicular, first find the slope of the line and
then take the negative inverse of that slope.  The inverse is found by dividing 1 by the slope
of the original line and once you find that inverse, multiply it by minus 1.
```