8y is less than or equal to -4x
8y < -4x
We draw the "equal to" part first, then we will draw the "less than"
part later.
First the "equal to" part
8y = -4x
We form this table of points by making up values of one letter,
substituting them and and solving for the other letter> Here are
three points:
point
x | y | (x,y)
0 | 0 | (0,0)
2 | -1 | (2,-1)
-4 | 2 | (-4,2)
Plot those:
Now we draw a solid line through those three points:
Now it's time to graph of the "less than" part.
Either all the points above the line are solutions and must
be shaded, or else none are, and all the points below the
line are solutions or none are.
All we have to do is pick any point that is not on the line.
That means we cannot pick any of the three points we plotted
to draw the line.
If we pick a test point above the line, say the point (1,3)
Then we substitute (x,y) = (1,2) into the inequality
8y < -4x
8(2) < -4(1)
16 < -4
That is false so we know that NONE of the solution are
above the line, and so all the solutions are below the
line and we should shade that part.
So the desired graph is:
But you should also notice that If we had picked a test point BELOW
the line, say the point (-2,-3)
and had substituted (x,y) = (2,-3) into the inequality
8y < -4x
8(-3) < -4(-2)
-24 < 8
That is true so we would know that ALL of the solution are
below the line, and so we should shade the region BELOW the
line. So regardless of which test point we pick, we will
always shade the same side of the line either way.
Edwin
