Elliptic curves on finite fields I've been reading: https://github.com/bellaj/Blockchain/blob/6bffb47afae6a2a70903a26d215484cf8ff03859/ecdsa_bitcoin.pdf

On page 22 it shows an eliptic curve over F17.



I have added the orange lines and labels.

Do the orange lines illustrate that a line through points at P(2,10) and Q(5,9) also intersects the "curve" at -R(12,1)?

i.e. Does the finite field version graphically match an elliptic curve over real numbers, with the provisos that the finite field curve is discontinuous and that lines wrap?

Or am I hopelessly confused about elliptic curves on finite fields (as I expect).

P.S. If this is an accurate graphical representation, how do I illustrate tangents to the discontinuous curve?

P.P.S. There are multiple lines which contain three points.  X, Y and -Z, in purple, are another (below).
You are correct about the graphical representation. A line in the finite field $\mathbb{F}_p$ is not $y=ax+b$ but "informally" $y \equiv ax+b \pmod p$, so the line "repeats" itself. For the tangent, you refer to the algebraic formula to trace the line.
Have a look at the third figure here.