document.write( "Question 1106028: Line L, passes through points P(n, 4) and Q(1 2), Line L, passes through points R(4, 3) and S (1, 5). a) What is the value of n if the lines are parallel? b) If the lines are perpendicular, what is the value of n? \n" ); document.write( "
Algebra.Com's Answer #720949 by greenestamps(13215)\"\" \"About 
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\n" ); document.write( "Obviously you are talking about two different lines., The line through points R and S is fixed, so let's call that the \"original\" line L. Then let's make M the line through P and Q parallel to line L and N the line through P and Q perpendicular to line L.

\n" ); document.write( "The slope of the fixed line L is \"%285-3%29%2F%281-4%29+=+-2%2F3\".

\n" ); document.write( "The slope of the first line is \"%282-4%29%2F%281-n%29+=+-2%2F%281-n%29+=+2%2F%28n-1%29\".

\n" ); document.write( "For the lines to be parallel, the slope of the first line has to be -2/3 -- the same as the slope of line L:
\n" ); document.write( "\"2%2F%28n-1%29+=+-2%2F3\"
\n" ); document.write( "\"6+=+-2n%2B2\"
\n" ); document.write( "\"4+=+-2n\"
\n" ); document.write( "\"n+=+-2\"

\n" ); document.write( "The lines are parallel when n is -2; line M passes through the points (-2,4) and (1,2).

\n" ); document.write( "For the lines to be perpendicular, the slope of the first line has to be 3/2 -- the negative reciprocal of the slope of line L:
\n" ); document.write( "\"2%2F%28n-1%29+=+3%2F2\"
\n" ); document.write( "\"4+=+3n-3\"
\n" ); document.write( "\"7+=+3n\"
\n" ); document.write( "\"n+=+7%2F3\"

\n" ); document.write( "The lines are perpendicular when n is 7/3; line N passes through the points (7/3,4) and (1,2).

\n" ); document.write( "The graph shows the original line L (red), passing through (1,5) and (4,3); line M which is parallel to L (green), passing through (-2,4) and (1,2); and line N which is perpendicular to L, passing through (1,2) and (7/3,4).

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