How do you determine the slope signs by just looking at 3D graphs?
We look at the slope in the positive direction of the $\displaystyle x$- and $\displaystyle y$-axes. If the surface is curving down, the slope is negative, if up, the slope is positive.
When you learn about directional derivatives, you will be able to calculate the slope in any direction, not just the positive direction of the $\displaystyle x$- and $\displaystyle y$-axes.