I have an elliptic curve $E = y^2 \equiv x^3 -2$ mod $7$. I added $(5, 5)+(5, 5)$ once and got $(6, 5)$. Now I am trying to add $(6, 5)+(5, 5)$. I know that I should get $(3, 2)$. However when I find the slope I get: $$ m = \frac{y_2-y_1}{x_2-x_1} = \frac{5-5}{6-5} = \frac{0}{1} $$ I take this to be $0$. Then I go calculate $$x_3 = m^2-x_1=x_2 = 0 - 6 - 5 = -11 = 3$$ and finally I go calculate $$y_3 = m(x_1 - x_3)-y_1 = 0(6-3) - 5 = 5$$ I am fairly confident that this is the wrong answer, so I am wondering where I am doing my calculation wrong for $y_3$?
For reference, I am trying to find $k*(5,5) = (3,5)$.
$0-5=2 \pmod{7}$, so $y_3=2$.