No, there is nothing special about 1 and 3, except that they are 
easy numbers to work with.  But you are free to choose ANY value 
for an x-coordinate to find the corresponding y-coordinate.  You 
are also free to choose ANY value for a y-coordinate to find the 
corresponding x-coordinate. However, if you choose very large 
numbers, you will have to make a very large graph, and if you 
choose values hard to work with, like fractions and decimals, 
the work will be harder.  But theoretically you can choose any 
numbers that you want to.

Every time you choose a number at random for one variable's 
coordinate, and substitute to find the other variable's 
coordinate, you have found another point on the SAME line.

Suppose we arbitrarily choose y = 4.  Then we substitute 4 for y in

y + x = -3
4 + x = -3
    x = -7

That gives us the point (x,y) = (-7,4), and we can plot it like this:

 

--

Now suppose we arbitrarily choose x = 5.  Then we substitute 5 for x in

y + x = -3
y + 5 = -3
    y = -8

That gives us the point (x,y) = (5,-8), and we can plot it like this:



--

Now suppose we arbitrarily choose y = -7.  Then we substitute -7 for y in

 y + x = -3
-7 + x = -3
     x =  4

That gives us the point (x,y) = (4,-7), and we can plot it like this:



Now suppose we arbitrarily choose x = -2.  Then we substitute -2 for x in

    y + x = -3
 y + (-2) = -3
    y - 2 = -3
        y = -1
     
That gives us the point (x,y) = (-2,-1), and we can plot it like this:



Now suppose we arbitrarily choose y = 2.  Then we substitute 2 for y in

    y + x = -3
    2 + x = -3
        x = -5
       
     
That gives us the point (x,y) = (-5,2), and we can plot it like this:



Now we lay a ruler along those points and we will
find they will all lie on a straight line, like
this green line below:



So you see we got the graph of the line without using 1 or 3.
But of course you can use 1 and 3 if you like.  Notice that you
only need two points to draw a line.  So you can draw the line
just by getting ANY two points on it.  However, since people do 
make mistakes, you should always get at least three points as 
a check, because if you were to get three points that are not 
in a straight line, then you would know that at least one of them 
was wrong.  But if you only get two points, you can always draw a
line through them, even if you made a mistake on one of them. So
if you are going to get just 2 points, be sure not to make a 
mistake!

Edwin