How do you graph using intercepts

What you do is you find both the x and y intercepts,
once you found these
mark them on the graph
then connect the points with a line. This only works with linear type graphs :)

so for
y = -3 - x
to find the x-int
let y = 0
0 = -3 - x
x = -3
to find the y-int
let x = 0
y = -3 - 0
y = -3

so for y = -3 - x we know two coordinates, the x and y intercepts: (-3, 0) and (0, -3)
mark both of these on your graph and connect the points (remember to extend the line beyond these points)

x + 4y = 10
to find x-int, let y = 0
x = 10
to find y-int, let x = 0
4y = 10
y = 10/4 or (2.5)
we know these coordinates: (10, 0) and (0, 2.5)
mark these on the graph and use your ruler to join these points and extend the graph beyond them

Hope this was helpful :)
If you need extra help, feel free to pm me :)