document.write( "Question 73691: Find an equation for line with y-intercept 3 that is perpendicular to the line y=(2/3)x-4.\r
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Algebra.Com's Answer #52890 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Find an equation for line with y-intercept 3 \r\n" );
document.write( "that is perpendicular to the line \r\n" );
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document.write( "\"y=%282%2F3%29x-4\"\r\n" );
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document.write( "Compare that to the \"slope y-intercept\" form\r\n" );
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document.write( "\"y=m%2Ax%2Bb\"\r\n" );
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document.write( "and you see that the slope is \"m=2%2F3\" \r\n" );
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document.write( "Now we use the rule:\r\n" );
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document.write( "If a line has slope \"A%2FB\" then \r\n" );
document.write( "1. A line parallel to it will ALSO have slope \"A%2FB\"\r\n" );
document.write( "2. A line perpendicular to it will have slope \"-B%2FA\"\r\n" );
document.write( "(Note: if the slope is a whole number and\r\n" );
document.write( "not a fraction, write it over 1, so it will be\r\n" );
document.write( "in the form \"A%2FB\")\r\n" );
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document.write( "A line perpendicular to a line with slope \"2%2F3\" will\r\n" );
document.write( "therefore by the 2nd rule above have slope \"-3%2F2\"\r\n" );
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document.write( "Now all we have to do is use the slope y-intercept form\r\n" );
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document.write( "\"y=m%2Ax%2Bb\"\r\n" );
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document.write( "this time with \"m=-3%2F2\" and \"b=3\", so we have\r\n" );
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document.write( "\"y=%283%2F2%29x%2B3\"\r\n" );
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document.write( "If \"f%28x%29=x%5E2+%2B+5\", Find \"f%28a%2Bb%29-f%28a%29\". \r\n" );
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document.write( "First find \"f%28a%2Bb%29\" by replacing \"x\" by \"%28a%2Bb%29\"\r\n" );
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document.write( "\"f%28a%2Bb%29=%28a%2Bb%29%5E2%2B5\"\r\n" );
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document.write( "Now find \"f%28a%29\" by replacing \"x\" by \"a\"\r\n" );
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document.write( "\"f%28a%29=a%5E2%2B5\"\r\n" );
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document.write( "So \"f%28a%2Bb%29-f%28a%29\" = \"%28%28a%2Bb%29%5E2%2B5%29-%28a%5E2%2B5%29\" = \"%28a%2Bb%29%5E2%2B5-a%5E2-5\" =\r\n" );
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document.write( "\"%28a%2Bb%29%5E2-a%5E2\" = \"%28a%2Bb%29%28a%2Bb%29-a%5E2\" = \"a%5E2%2Bab%2Bab%2Bb%5E2-a%5E2\" =\r\n" );
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document.write( "\"2ab%2Bb%5E2\"\r\n" );
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document.write( "Edwin
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