document.write( "Question 254181: Find the equation of the line with slope -1 that is the tangent to the curve y=1/x-1. \n" ); document.write( "
Algebra.Com's Answer #186510 by drk(1908)\"\" \"About 
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The question was: slope -1 that is the tangent to the curve y=1/x-1
\n" ); document.write( "step 1 - take the derivative of y to get
\n" ); document.write( " (i) y' = \"%28%28x-1%29%2A0+-+1%2A%281%29%29+%2F+%28x-1%29%5E2\"
\n" ); document.write( "which simplifies to
\n" ); document.write( "(ii) y' = \"%28+-+1%29+%2F+%28x-1%29%5E2\".
\n" ); document.write( "Now slope = -1 means derivative = -1. We get from (ii)
\n" ); document.write( "(iii) \"-1+=+-1%2F%28x-1%29%5E2\"
\n" ); document.write( "Solving we get
\n" ); document.write( "(x-1)^2 = 1
\n" ); document.write( "(x-1) = +-1
\n" ); document.write( "X = 0 or x = 2
\n" ); document.write( "We have two coordinates: (0,1) and (2,1)
\n" ); document.write( "So, we have y = mx + b with (0,1) to get
\n" ); document.write( "1 = 0*-1 + b
\n" ); document.write( "b = 1
\n" ); document.write( "The first equation is
\n" ); document.write( "Y = -1x + 1.
\n" ); document.write( "Now, we have y = mx + b with (2,1) to get
\n" ); document.write( "1 = 0*2 + b
\n" ); document.write( "b = 1
\n" ); document.write( "The second equation is
\n" ); document.write( "Y = -1x + 1.
\n" ); document.write( "So, it appears that we have
\n" ); document.write( "Y = -1x + 1 \n" ); document.write( "
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