Graph the inequality
x - 3y < 9
First form the equation of the boundary line,
which is found by replacing the < by =
x - 3y = 9
Draw this line by find the intercepts (0,-3) and (9,0)
Draw the line dotted because the inequality is
< and not <
Now we only have to decide whether we are to shade the
upper side of the line or the lower side of it. To do
this we pick any point which IS NOT on the line. Say we
choose as a test point the point (2,3) marked below with
an o, which is above the line.
Now we substitute
(x,y) = (2,3) into the inequality
x - 3y < 9
If we get a true inequality, then we will shade the
same side of the line that the test point is on. If
we get a false equationj, we shade the other side:
x - 3y < 9
2 - 3(3) < 9
2 - 9 < 9
-7 < 9
This is true, so we shade the same side of the line
which the test point that we picked is on, namely the
upper side. I can't shade on here but you can on
your paper:
Edwin
