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For what value(s) of k the lines y=(k+1)x-3 and (2k-1)x+1 are parallel
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\n" ); document.write( "Recognizing this in the form y = mx + b
\n" ); document.write( "You are given 2 slopes: m1 = (k+x) and m2 = (2k-1)
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\n" ); document.write( "Parallel lines have equal slopes, therefore we can find k like this:
\n" ); document.write( "(2k-1) = (k+1)
\n" ); document.write( "2k - k = 1 + 1
\n" ); document.write( "k = 2
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\n" ); document.write( "Substitute 2 for k in both equation and you can see they have equal slopes
\n" ); document.write( "y = 3x - 3 and y = 3x + 1
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\n" ); document.write( " and are perpendicular?
\n" ); document.write( "The slope relationships of perpendicular lines are m1 * m2 = -1
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\n" ); document.write( "(k+1) * (2k-1) = -1
\n" ); document.write( "FOIL
\n" ); document.write( "2k^2 + k - 1 = -1
\n" ); document.write( "2k^2 + k - 1 + 1 = 0
\n" ); document.write( "2k^2 + k = 0
\n" ); document.write( "Factor out k
\n" ); document.write( "k(2k+1) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "k = 0
\n" ); document.write( "and
\n" ); document.write( "2k = -1
\n" ); document.write( "k = -.5
\n" ); document.write( "Find the two equations when k = 0
\n" ); document.write( "y = 1x - 3 and y = -1x + 1 are perpendicular
\n" ); document.write( "and
\n" ); document.write( " when k = -.5
\n" ); document.write( "The two equations: y = .5x - 3, and y = -2x + 1 also are perpendicular
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\n" ); document.write( "Did this make sense to you, any questions?? \n" ); document.write( "