How do you know if a line has a negative, positive, zero or undefined slope?

Starting with a slope of zero , the line will always be horizontal and majority of the time will only pass through the y axis 
In the equation there is no " x" 
ex. y=2

For an Undefined Slope the line will always be vertical , going up and down and for majority of the time only coming in contact with the x axis 
In this equation there is no " y" 
ex. x= 9

For Positive Slope , line should be diagonal if linear and will increase the x and y coordinates , this equation contains both the y and x and passes through both the y and the x axis.. the movement of the positive slope is upward 

For Negative Slope, same as positive the line should be diagonal if linear, but now the x and y coordinates should decrease and the movement of the line is downward , the line passes through both the y and the x axis

How to Find Slope 

Δy over Δx 
the triangle refers to the change in 
ex.  A (2,-3) B ( 4, -5 )

-3- (-5) / 2-4 
2/-2
-1 

Since the number is negative then the slope is negative and going downward

I hope the long explanation helped!