Slope is such and easy thing to teach and I see so many math teachers make it so difficult!
Here is the bottom line. Instead of getting the students to memorize the rise and run rules of "up and to the right and down and to the left being the same and positive" and vise verse for the negative Slope. Teach it to them like this...
Say this to them...
In English we read from Left to Right (they know that and will never forget it!) correct?
They say yes!
Okay, here's the easy way to remember the 4 Slope types.
1.) If the Slope is going up hill from left to right it's positive. Simple, you're walking up the hill from left to right. That's just how we do it when reading charts and English, Left to right!
I then draw a miserable little person trying to push a ball up a positive Slope.
2.) Then I ask how many of them ski or snowboard sled ride etc. They all do of course...
You want to do this down hill right?
So from left to right just like before if we are going down hill the Slope would be negative. Makes sense right? You're going down hill that should be negative.
3.) What if we were walking on flat floor? What Slope would that be? Zero! There is no pitch to the floor positive or negative. So, it's zero!
4.) There is also an undefined Slope. Here's how you get them to remember it.
How many of you are Spider-Man? Can walk up walls.
Of course there is one student who says "I am"
Okay, if you can walk up the wall what Slope would that be? It's not up hill and it's not down hill. So if you can't walk on it then how do you describe it? If you tried to walk up or down it you would fall off either way right?
This is an undefined Slope. It is NOT zero Slope!
TIP: You can also show them sample slopes with numbers where they have a zero on top and then another with a zero on the bottom. You remind them they may not divide by zero. Which is undefined.
Make sure they master the difference between zero Slope and undefined Slope before you move on.
Once they grasp the we always read from left to right concept, they will not struggle with differentiating between positive and negative.
Now when they go to graph a line using slope intercept form they will be able to know when to go "up and to the right" or "up and to the left" because they will know by the sign of the slope whether it needs to be going up hill or down hill.