document.write( "Question 237520: How do you find the tangent and normal lines of something that starts out as x^2-4x and has a derivative of 2x-4\r
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Algebra.Com's Answer #174663 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "You have to have a place where you want the tangent and normal lines defined. That is, you can specifically answer the question: \"Derive equations of the tangent and normal lines to the graph of at the point \"\r
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\n" ); document.write( "\n" ); document.write( "The first derivative is, as you stated, , and tells us the slope of the tangent line at any value of in the domain of the original function.\r
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\n" ); document.write( "\n" ); document.write( "So, in general, at the point , the slope of the tangent line is . The normal line at the same point is the line perpendicular to the tangent at that point. Since perpendicular lines have negative reciprocals, that is:\r
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\n" ); document.write( "\n" ); document.write( "We can say that the slope of the normal line at is \r
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\n" ); document.write( "\n" ); document.write( "Now all you need is the point-slope form of the equation of a straight line to derive the desired equations:\r
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\n" ); document.write( "\n" ); document.write( ": Tangent\r
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