document.write( "Question 593813: how do I find the equation of the line with a slope -1 that is tangent to the curve y=1/x-1?\r
\n" ); document.write( "\n" ); document.write( "I don't think there is a solution to this since there are two curves and the y-axis is a vertical asymptote.\r
\n" ); document.write( "\n" ); document.write( "Any help is greatly appreciated. \n" ); document.write( "
Algebra.Com's Answer #376468 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
how do I find the equation of the line with a slope -1 that is tangent to the curve y=1/x-1?
\n" ); document.write( "Find the derivative of:
\n" ); document.write( "y=1/x-1
\n" ); document.write( "y=x^(-1)-1
\n" ); document.write( "y' = -x^(-2)
\n" ); document.write( "y' = -1/x^2
\n" ); document.write( ".
\n" ); document.write( "Set y' to -1 and solve for x:
\n" ); document.write( "y' = -1/x^2
\n" ); document.write( "-1 = -1/x^2
\n" ); document.write( "x^2 = 1
\n" ); document.write( "x = {-1, +1}
\n" ); document.write( ".
\n" ); document.write( "Using x=1, find y:
\n" ); document.write( "y=1/x-1
\n" ); document.write( "y=1/1-1
\n" ); document.write( "y=1-1
\n" ); document.write( "y=0
\n" ); document.write( "so, the point at which the slope is -1 is at (1,0)
\n" ); document.write( ".
\n" ); document.write( "equation of line, plug into the \"point-slope\" form:
\n" ); document.write( "y - y1 = m(x - x1)
\n" ); document.write( "y - 0 = -1(x - 1)
\n" ); document.write( "y = -x + 1 (this is what they're looking for)
\n" ); document.write( " \n" ); document.write( "
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