What does the line y = -3x - 3 look like?

Using the general format of a line, y = mx + c,
Where m = slope of the line, c = vertical intercept.

y = -3x -3, comparing to y = mx + c
Slope, m = -3,  vertical intercept, c = -3.

For a negative slope, the line would be falling downwards from the left hand side of graph sheet to right hand side.

Slope = -3,

Vertical or y intercept is the point it cuts across the y axis, at this point, x = 0
y intercept =    (0, -3)

x intercept, at this point, the value of y is zero.

y = -3x - 3

0 = -3x - 3

0 + 3x = -3

3x = -3

x = -3/3

x = -1.

x intercept       =         (-1, 0)
  
 So we would plot the points  (0, -3) and (-1, 0)

See attached picture for sketch of the line y = -3x - 3.