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.
one
1 straight line. An infinite number of curved lines.
Just one.
3
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.
3
4*3/2 = 6 lines.
# 1
15 lines.
Three
Since the question does not require them to be straight lines, the answer is infinitely many.