In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary.
Even in the Euclidean plane, two points determine infinitely many lines that are not straight!
5 its 4
If two lines have different slopes, then they intersect at exactly one point. It makes no difference what their y-intercepts are.
1 straight line. An infinite number of curved lines.
As long as at least two of them are different points, exactly one line.
Three lines are determined by three points unless the points are all on the same line ( i.e. co-linear)
Any three non-collinear points will define a single plane. A plane is composed of an infinite number of distinct lines.
Exactly one plane in each case.
There are 13*12/2 = 78 lines.
4*3/2 = 6 lines.
Since the question does not require them to be straight lines, the answer is infinitely many.