document.write( "Question 1129389: Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1, k+1) and (3,5) \n" ); document.write( "
Algebra.Com's Answer #745953 by MathLover1(20849)\"\" \"About 
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Find \"k\" so that the line through (\"7\",\"2k\") and (\"4\",\"-3\") is parallel to the line through (\"1\", \"k%2B1\") and (\"3\",\"5\") \r
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\n" ); document.write( "\n" ); document.write( "use a slopes:\r
\n" ); document.write( "\n" ); document.write( "a slope of the line through (\"7\",\"2k\") and (\"4\",\"-3\") is:\r
\n" ); document.write( "\n" ); document.write( "\"m=%28-3-2k%29%2F%284-7%29\"\r
\n" ); document.write( "\n" ); document.write( "\"m=%28-3-2k%29%2F%28-3%29\"\r
\n" ); document.write( "\n" ); document.write( "a slope of the parallel to the line that passes through (1, k+1) and (3,5) is:\r
\n" ); document.write( "\n" ); document.write( "\"m%5Bp%5D=%285-%28k%2B1%29%29%2F%283-1%29\"\r
\n" ); document.write( "\n" ); document.write( "\"m%5Bp%5D=%285-%28k%2B1%29%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"m%5Bp%5D=%285-k-1%29%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"m%5Bp%5D=%284-k%29%29%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "since parallel lines have same slope, we have:\r
\n" ); document.write( "\n" ); document.write( "\"m=m%5Bp%5D\"\r
\n" ); document.write( "\n" ); document.write( "\"%28-3-2k%29%2F%28-3%29=%284-k%29%2F2\"....cross multiply\r
\n" ); document.write( "\n" ); document.write( "\"2%28-3-2k%29=%28-3%29%284-k%29\"\r
\n" ); document.write( "\n" ); document.write( "\"-6-4k=-12%2B3k\"\r
\n" ); document.write( "\n" ); document.write( "\"-6%2B12=4k%2B3k\"\r
\n" ); document.write( "\n" ); document.write( "\"6=7k\"\r
\n" ); document.write( "\n" ); document.write( "\"k=6%2F7\"\r
\n" ); document.write( "\n" ); document.write( "so, slope is
\n" ); document.write( "\"m=%28-3-2%286%2F7%29%29%2F%28-3%29\"
\n" ); document.write( "\"m=%28-3-12%2F7%29%2F%28-3%29\"
\n" ); document.write( "\"m=11%2F7\"\r
\n" ); document.write( "\n" ); document.write( "same for parallel line
\n" ); document.write( "\"m%5Bp%5D=%2811%2F7%29\"\r
\n" ); document.write( "\n" ); document.write( "then, points and slope for one line are:
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\n" ); document.write( " (\"7\",\"2%286%2F7%29\") and (\"4\",\"-3\")
\n" ); document.write( "=>(\"7\",\"12%2F7\") and (\"4\",\"-3\") \r
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\n" ); document.write( "\n" ); document.write( "equation of this line is: use point-slope formula
\n" ); document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\".......if (\"4\",\"-3\") \r
\n" ); document.write( "\n" ); document.write( "\"y-%28-3%29=%2811%2F7%29%28x-4%29\"\r
\n" ); document.write( "\n" ); document.write( "\"y%2B3=%2811%2F7%29x-%2811%2F7%294\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%2811%2F7%29x-44%2F7-3\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%2811%2F7%29x-44%2F7-21%2F7\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%2811%2F7%29x-65%2F7\"-> one line\r
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\n" ); document.write( "\n" ); document.write( "equation of the parallel line is: use point-slope formula\r
\n" ); document.write( "\n" ); document.write( "(\"1\", \"6%2F7%2B1\") and (\"3\",\"5\")
\n" ); document.write( "=> (\"1\", \"13%2F7\") and (\"3\",\"5\") \r
\n" ); document.write( "\n" ); document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\".......if \"m%5Bp%5D=%2811%2F7%29\"and (\"3\",\"5\") \r
\n" ); document.write( "\n" ); document.write( "\"y-5=%2811%2F7%29%28x-3%29\"\r
\n" ); document.write( "\n" ); document.write( "\"y-5=%2811%2F7%29x-%2811%2F7%293\"\r
\n" ); document.write( "\n" ); document.write( "\"y-5=%2811%2F7%29x-33%2F7\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%2811%2F7%29x-33%2F7%2B5\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%2811%2F7%29x-33%2F7%2B35%2F7\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%2811%2F7%29x%2B2%2F7\"-> parallel line\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=>(\"7\",\"12%2F7\") and (\"4\",\"-3\")
\n" ); document.write( "=> (\"1\", \"13%2F7\") and (\"3\",\"5\") \r
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