help me in this

(x-y)^2 =2x+1      expand

x^2 - 2xy + y^2  = 2x + 1       using implicit differentiation, we have

2x - 2y - 2xy' + 2yy'  = 2         divide through by 2

x - y - xy'  + yy'   = 1

y' [ y - x]  = 1 + y  - x

y'  =     [  1 + y  - x ] / [ y - x ]

And the slope at (4,1)  =

y'  = [ 1 + 1  - 4] / [ 1 - 4] =    [ -2]  / [ -3]   =   2/3

So the equation is

y = [2/3]( x - 4) + 1

y = [2/3] x - 8/3 + 1

y = [2/3]x  -5/3

Here's the graph of the function and the tangent line...........https://www.desmos.com/calculator/igebscsto1