# 10) Find the equation of all lines having slope –1 that are tangents to the curve

We know that the slope of the tangent of at the point of the given curve is given by

Given the equation of curve is

It is given thta slope is -1
So,

Now, when x = 0 ,
and
when x = 2 ,
Hence, the coordinates are (0,-1) and (2,1)
Equation of line passing through (0,-1) and having slope = -1 is
y = mx + c
-1 = 0 X -1 + c
c = -1
Now equation of line is
y = -x -1
y + x + 1 = 0
Similarly, Equation of line passing through (2,1) and having slope = -1 is
y = mx  + c
1 = -1X2 + c
c = 3
Now equation of line is
y = -x + 3
y + x - 3 = 0

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