Thread: equation of a tangent line

Originally Posted by missfuzzy

I have this question, Find equation of the line with a slope of -1 that is tangent to y = 1/x - 1.

Is this y= (1/x)- 1 or y= 1/(x-1)?

[tex] This is what i have so far, I know that y = mx + b and therefore y = -1x + k. and that to set the y values equal to each other to get; 1/x-1 = -1x + k. Then I get stuck on rearranging this equation so that it equals zero, I know schoolgirl error, once the equation is rearranged i can use the discriminant part of the quadratic equation to solve for k, (b^2 - 4ac), when this equals zero there is just one solution to the quadratic, right. But it is just that rearranging part that is getting me stuck, im not sure off it.[/QUOTE]
Since you know the slope of the tangent line is -1, you know the derivative of y must be -1 at that point. For what x is the derivative -1?

Will the tangent line be unique if the original function is ? Because