You can represent an inequality on a graph There are some important rules to follow If the inequality is or the boundary line for the region is shown by a solid line If the inequality is gt or lt the boundary line for the region is shown as a ID: 142542
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Slide1
REPRESENTING LINEAR INEQUALITIES ON GRAPHSSlide2
You can represent an inequality on a graph.
There are some important rules to follow.
If the inequality is ≥ or ≤ the boundary line for the region is shown by a
solid
line.
If the inequality is > or < the boundary line for the region is shown as a
broken
(dashed) line.
You are expected to shade the
unwanted
region. (This will leave the required region clear.)Slide3
y
x
-2
-4
-4
-2
2
2
4
4
Examples
1
Show the region
x
≥ 2 on a graph. Leave the required region unshaded.
First draw the boundary line
x
= 2.
The line will be
solid
because
of the ≥ symbol.
required region
Remember to shade the
unwanted
region.Slide4
y
x
-2
-4
-4
-2
2
2
4
4
Examples
2
Show the region
y
< 3 on a graph. Leave the required region unshaded.
First draw the boundary line
y
= 3.
The line will be
dashed
because
of the < symbol.
required region
Remember to shade the
unwanted
region.Slide5
y
x
-2
-4
-4
-2
2
2
4
4
Examples
3
Show the region -3 ≤
x
< 2 on a graph. Leave the required region unshaded.
First draw the boundary lines
x
= -3 and
x
= 2.
The line x = -3 will be
solid
because of the ≤ symbol.
required region
Remember to shade the
unwanted
regions.
The line x = 2 will be
dashed
because of the < symbol.Slide6
y
x
-2
-4
-4
-2
2
2
4
4
Examples
4
Show the region
x
+
y
< 2 on a graph. Leave the required region unshaded.
First draw the boundary line
x
+
y
= 2.
The line will be
dashed
because
of the < symbol.
required region
Remember to shade the
unwanted
region.
x
0
2
y
2
0Slide7
y
x
-2
-4
-4
-2
2
2
4
4
Examples
5
Show the region
y
≥ 2
x
+1 on a graph. Leave the required region unshaded.
First draw the boundary line
y = 2x +
1.
The line will be
solid
because
of the ≥ symbol.
required region
Remember to shade the
unwanted
region.
x
0
1
2
y
1
3
5Slide8
6
A region R, contains points whose coordinates satisfy the following inequalities.
x
≥ -4
y
> -1
x
+ 2
y
≤ 2 On a graph draw suitable lines and label the region R.
y
x
-2
-4
-4
-2
2
2
4
4
Examples
First show the region
x
≥ -4 on the graph (remember to shade the unwanted region).
x
0
2
y
1
0
Next show
y
> -1 (remember to
shade the unwanted region).
Then show
x
+ 2
y
≤ 2 (remember
to shade the unwanted region).
R