Question

3-35. Fisher thinks that any two lines must have a point of intersection. Is he correct? If so, explain how youknow. If not, produce a counterexample. That is, find two lines that do not have a point of intersection and explainhow you know

Answer 1

Any two lines must have a point of intersection, with ONLY ONE exception : when the lines are parallel. That means they have exactly the same inclination or Slope.

As an example of two lines that hasnt point of intersection they are

y = 5x + 16

y = 5x + 11

We know both lines have no point of intersection because

both have the same slope or inclination m. By comparation with slope intercept equation

y = mx + b

then we see both have same inclination, and b is 11 in one line and 16 in the other line. This means both lines are parallel with one line going over the other line, without touching it in any point.