"steep slope" when cold fronts encounter warm fronts: Confusing sentence in textbook
The slope is the ratio of the vertical to horizontal distance.

From here 


  "Warm fronts have a gentler slope and generally move more slowly than cold fronts, so the rising motion along warm fronts is much more gradual."


You can see the steep slope of a cold front visualized, 

and a more gradual slope for the warm front:



But depending on the source, there seems to be varying definitions of what the slope value actually is.  It makes sense, given that the answer would be different depending on how deep you go into the front and there would be seasonal variability.  

This site has a nice example:


  "The cold front is steepest in the lowest several hundred meters of the atmosphere with a slope of about 1/100, meaning that elevation increases about 1 kilometer for every 100 kilometers of horizontal distance from the surface front. Then the upward slant relaxes into a much more gentle slope (e.g. 1/300). All along the upward slant of the cold wedge, cold air abuts with warmer air, creating an upward-slanting boundary characterized by large temperature contrasts."