document.write( "Question 1010002: Find two values of k such that the points (-3,4), (0,k), and (k,10) are collinear. \n" ); document.write( "
Algebra.Com's Answer #625489 by MathLover1(20849)\"\" \"About 
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Find two values of k such that the points (\"-3\",\"4\"), (\"0\",\"k\"), and (\"k\",\"10\") are collinear. \r
\n" ); document.write( "\n" ); document.write( "the points are collinear if they lie on same line\r
\n" ); document.write( "\n" ); document.write( "use the slope of a line to find \"k\"\r
\n" ); document.write( "\n" ); document.write( "\"slope+=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r
\n" ); document.write( "\n" ); document.write( " for the points (\"-3\",\"4\"), (\"0\",\"k\"),\r
\n" ); document.write( "\n" ); document.write( "\"slope+=%28k-4%29%2F%280-%28-3%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"slope+=%28k-4%29%2F%280%2B3%29\"\r
\n" ); document.write( "\n" ); document.write( "\"slope+=%28k-4%29%2F3\".............eq.1\r
\n" ); document.write( "\n" ); document.write( "for (\"0\",\"k\"), and (\"k\",\"10\")\r
\n" ); document.write( "\n" ); document.write( "\"slope+=%2810-k%29%2F%28k-0%29\"
\n" ); document.write( "\"slope+=%2810-k%29%2Fk\" ............eq.2\r
\n" ); document.write( "\n" ); document.write( "from eq.1 and eq.2 we have\r
\n" ); document.write( "\n" ); document.write( "\"%28k-4%29%2F3=%2810-k%29%2Fk\"............cross multiply\r
\n" ); document.write( "\n" ); document.write( "\"%28k-4%29%2Ak=3%2810-k%29\"\r
\n" ); document.write( "\n" ); document.write( "\"k%5E2-4k=30-3k\"
\n" ); document.write( "\"k%5E2-4k%2B3k-30=0\"
\n" ); document.write( "\"k%5E2-k-30=0\"...........factor completely\r
\n" ); document.write( "\n" ); document.write( "\"k%5E2-6k%2B5k-30=0\"
\n" ); document.write( "\"%28k%5E2-6k%29%2B%285k-30%29=0\"
\n" ); document.write( "\"k%28k-6%29%2B5%28k-6%29=0\"
\n" ); document.write( "\"%28k-6%29+%28k%2B5%29+=+0\"\r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28k=6%29\"
\n" ); document.write( "\"highlight%28k=-5%29\"\r
\n" ); document.write( "\n" ); document.write( "so, the points (\"-3\",\"4\"), (\"0\",\"6\"), and (\"6\",\"10\") are collinear
\n" ); document.write( "and the points (\"-3\",\"4\"), (\"0\",\"-5\"), and (\"-5\",\"10\") are collinear\r
\n" ); document.write( "\n" ); document.write( "now find slope
\n" ); document.write( "\"slope+=%28k-4%29%2F3\".............eq.1 if \"highlight%28k=6%29\"
\n" ); document.write( "\"slope+=%286-4%29%2F3\"
\n" ); document.write( "\"highlight%28slope+=2%2F3%29\"\r
\n" ); document.write( "\n" ); document.write( "\"slope+=%28k-4%29%2F3\".............eq.1 if \"highlight%28k=-5%29\"
\n" ); document.write( "\"slope+=%28-5-4%29%2F3\"
\n" ); document.write( "\"slope+=-9%2F3\"
\n" ); document.write( "\"highlight%28slope+=-3%29\"\r
\n" ); document.write( "\n" ); document.write( "so, there are \"two\" possible lines and they are\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28y=%282%2F3%29x%2Bb%29\" and
\n" ); document.write( "\"highlight%28y=-3x%2Bb%29\"\r
\n" ); document.write( "\n" ); document.write( "we need y-intercepts \"b\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%282%2F3%29x%2Bb\" use one point : (\"0\",\"6\")\r
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\n" ); document.write( "\n" ); document.write( "\"6=%282%2F3%290%2Bb\"
\n" ); document.write( "\"b=6\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%282%2F3%29x%2B6\" and \r
\n" ); document.write( "\n" ); document.write( "\"y=-3x%2Bb\" use one point : (\"0\",\"-5\")
\n" ); document.write( "\"y=-3x-5\" \r
\n" ); document.write( "\n" ); document.write( "so, the line \"y=%282%2F3%29x%2B6\" contains points the points (\"-3\",\"4\"), (\"0\",\"6\"), and (\"6\",\"10\") \r
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\n" ); document.write( "\n" ); document.write( "and the line \"y=-3x-5\" contains points the points (\"-3\",\"4\"), (\"0\",\"-5\"), and (\"-5\",\"10\")\r
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