# How can you show that each new line drawn on a plane creates another $k+1$ regions? [duplicate]

The questions is

If $n$ straight lines are drawn on a plane such that each line intersects every other line and no three lines have a common point of intersection, then the plane is divided into $$\frac{n(n+1)}{2}+1$$ regions. Prove this by using mathematical induction.

I did the base case, but I do not know how to show that if $P(k)$ is true, then $P(k+1)$ is true. The worked solutions say that the addition of another line creates another $k+1$ regions. How do they get that?

Thanks