Output an upside-down tent
MATL, 55 53 52 51 bytes
|95cy4*Y&quot;DXytPEt0*yvG0&gt;?P_]!'\/ 'w)95JG|G0&lt;yEq:++&amp;(

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Explanation
Let N denote the input. The code proceeds in three steps.
First, the first line of  4*N underscores is built as a string and is displayed (which removes it from the stack).
Second, the &quot;frame&quot; of the tent is built using the two types of slashes. To do this, a numerical 2D array is created which contains 1 and 2 corresponding to the two types of slashes, and 0 for space.
This is done concatenating four matrices:

An identity matrix of size abs (N);
A matrix of the same size containing 2 in the antidiagonal;
A null matrix of the same size;
A copy of matrix 2.

Concatenating these four matrices vertically gives, using N=3 as an example, the following 4*N × N matrix:
1 0 0
0 1 0
0 0 1
0 0 2
0 2 0
2 0 0
0 0 0
0 0 0
0 0 0
0 0 2
0 2 0
2 0 0

(which, transposed, begins to look like the tent).
We now take care of the sign of the input. If it is positive we simply transpose the above matrix and index into the string '\/ '. Indexing is 1-based and modular, so 1 becomes '\', 2 becomes '/' and 0 becomes ' ', producing the 2D char array
\    /     /
 \  /     / 
  \/     /  

On the other hand, if the input is negative we vertically flip and arithmetically negate the 4*N × N matrix, producing
-2  0  0
 0 -2  0
 0  0 -2
 0  0  0
 0  0  0
 0  0  0
-2  0  0
 0 -2  0
 0  0 -2
 0  0 -1
 0 -1  0
-1  0  0

Index -1 now refers to '/' and -2 to '\'. That is, the two types of slashes have been interchanged, as required. Again transposing and indexing into the string '\/ ' thus gives the reversed tent:
\     \    /
 \     \  / 
  \     \/  

Third, underscores need to be filled into part of the last row of the 2D char array. The horizontal position of this line depends on the sign of the input, and its lenght is abs(N).
Once the corresponding spaces have been replaced by underscores, the result is implicitly displayed, below the initial line of underscores that was already displayed in the first step.