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A short review on graphing inequalities.
In order to graph the inequality y > 3 – x first graph the equation
y = 3 – x. This line will be the borderline between the points that
make y > 3 – x and the points that make y < 3 – x.
In y = mx + c form
we have y = -x + 3.
In this case we have
a line whose slope is
–1 and whose yintercept is 3.
4.0
y
2.0
-4.0
-2.0
2.0
-2.0
Now we have to decide which side
of the line satisfies y > 3 – x.
-4.0
4.0
x
A short review on graphing inequalities.
All we have to do is to choose one point that is off the line and
test it in the original inequality. If the point satisfies the
inequality then we are on the correct side of the line and we
shade that side. If the point does not satisfy the line, we shade
the other side.
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The most popular
point to use in the
shading test is (0, 0).
THE TEST: substitute
(0, 0) into y > 3 – x
and see if you get a
true statement.
2.0
-4.0
-2.0
2.0
-2.0
-4.0
0>3-0
y
0 > 3, which is false.
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x
Since (0, 0) did not satisfy the inequality y > 3 – x we conclude
that (0, 0) is on the wrong side of the tracks and we shade the other
side. Our conclusion is that every point in the shaded area is part
of the solution set for y > 3 – x.
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You can reinforce this idea
by testing several points in
the shaded area.
(2, 2)
2>3–2
2>1
(0, 3)
3>3–0
3>3
(4, 1)
1>3–4
y
2.0
-4.0
1 > -1
Each point that we pick in the shaded
area generates a true statement.
-2.0
2.0
-2.0
-4.0
4.0
x