Lineweaver Burk plots

I am confused about the competitive inhibition plots. Can someone explain why the slope increased? I found the below answer but it still doesn't make sense. Why would km going up increase the y intercept? If this is the case then if Km goes down wouldn't Y go up, and the slope go down? This is not what happens in non competitive plots for example. Sorry for the long post but this topic is really confusing me.

If your enzyme of choice is busy interacting with the competitive inhibitor...

Lineweaver Burk plots