5x + y = -1

Solve for y by adding -5x to both sides:

 5x + y = -1
-5x       -5x
--------------
      y = -5x - 1

Compare to

      y = mx + b

The slope is m = -5 and the line intercepts the y-axis at b = -1.

Plot the y-intercept on the y-axis at -1.


                                                  -5
Since the slope is -5, we write it as a fraction ———— 
                                                   1
From the y intercept we draw a vertical line the
number of units indicated by the numerator of the slope, which
is -5.  Since it is negative we draw the vertical line DOWNWARD.
I'll draw it in green:

(when the slope is positive we draw the line UPWARD from the y-intercept.)



From the end of that line, we draw a horizontal line to the
right which is the number of units long indicated by the 
denominator, which is 1.  So we now have:



Fionally get a ruler and draw a line through the y-intercept and
the end of the horizontal green line:




That's the graph.

Edwin