Java Coordinates

I am in an intro level programming class which uses Java (along with BlueJ).

Today we had to manipulate a line in the Java coordinate plane (sorry, I don't know the jargon).

Everything was going fine until I had to figure out the slope of the line. Due to the way the Java coordinates are laid out - (0,0) in the top left corner with values increasing to the bottom right corner - the slope worked the opposite as expected (specifically the 'y' or 'rise' value).

I ended up getting this right. As I view it, we are working in Quadrant 4 of a Cartesian plane, so I had to negate the run value: (It looked something like: int run = -(y2-y1)).

In some part, I understand this, but I am also having a difficult time visualizing this fully. Can anyone help me visualize this a bit more?

I know this is a tad vague, but I really am at a loss for how to fully explain my confusion (which is no doubt part of the confusion).

This is how I think about it: you've got a model and a view. The model represents...well the model - in your case, a line from point A to point B in your coordinate space. The view displays what the model represents. The way in which you described, it seems you are taking the model, placing it in the view, then extrapolating properties of the model from the view. Another way is to extrapolate the properties (slope) of the model directly from the model rather than indirectly through the view. This is an example of a pattern in programming termed MVC (model-view-controller). The view displays the model, any properties you wish to gather is done so directly through the model, and to take the concept one step further the controller (C) extrapolates interaction from the view to change the model.