the equation y=-x - 3 is in standard slope intercept form y=mx + b where b is the y intercept = -3, or the point (0,-3) when x=0, and m= slope = coefficient of the x terms when the linear equation is solved for y.
the x intercept is when y=0
then x= -3 which is the point (-3,0)
set x=0 and you find the y intercept = -3
set y=0 and you get the x intercept =-3
graphically plot those two points (0,-3) and (-3,0) and draw a line through them, That's the graph of the equation, y=-x-3