In Super Mario World, you can press down on the D pad while on a slope to slide down or up it, although you will lose momentum sliding up. In Super Mario World, the speed gained at sliding speed is greater than mario's maximum run speed. Because of this, if you jump from sliding on a slope, your speed will decrease if you press left or right after jumping. Your speed will decrease every frame your holding right or left and every frame you are touching flat, non-icy ground without sliding. This is important to know in Kaizo because many levels make you maintain slope speed. For these levels you want to slide, then go neutral on the D pad to maintain your speed. Additionally the level may require you to jump quickly off the ground you land on to make sure you maintain that speed to make larger jumps.
Additionally, Mario can kill may enemies and sprites by sliding into them on a slope, either up or down the slope. Using mario's slide, he can kill many enemies not normally capable of being killed by Mario, such as buzz saws, bouncing fireballs and even big boos.
When on a slope, tap down on the D Pad to begin sliding. The down button does not to be held to maintain the slide, this can be useful to know to avoid accidental left right inputs that can steal momentum. If you need to maintain slope spreed through multiple jumps, make sure to press the appropriate jump button as soon as you touch the ground, the sooner you press it, the more speed mario will maintain.