Find k so that the line through (3, -1) and (k, 2) is parallel to 12x+13y=26

Rewrite the equation to y-int form: y = (-12/13) x + 2.
Since they are parallel, they have the same slope, m = -12 / 13.

Plug (3,-1) into a new line y=mx+b with m = -12/13.
Solve for b:
-1 = (-12/13)(3) + b;
b = 23/13;

Now the new line becomes y = (-12/13) x + (23/13).
We can plug in the second point to find k:
2 = (-12/13) k + 23/13;
k = -1/4.