The slope is defined as the change in y/change in x ...
The y variable is the dependent variable, the x variable is the independent variable (you plug in values of x to get your y).
Given, the independent "x" change is increasing (or +) and the dependent "y" change is decreasing (-),
your slope is: ( - )/ ( + ) = ( - ).
If they were both increasing ... ( + )/ ( + )
or both decreasing ( - )/ ( - )
the slope would be positive.