Graphing Inequalities
On the Coordinate Plane
Remember your inequality symbols:
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to
Graphing inequalities on the xy­
axes is very similar to graphing
lines.
The process in the beginning is
the same...
Graphing an inequality
*get "y" by itself if needed(like y = mx + b)
1. use m and b to plot points
2. choose a solid or dotted line
3. choose a test point
4. shade
This is where the changes begin...
When graphing:
< or > then the line will
If the inequality is
be a DOTTED
LINE
If the inequality is ≤
a or ≥ then the
line will be aSOLID
LINE
Using a test point not on the line, plug it
back into the original inequality.
If the inequality is
true, SHADE
ON
THE SAME SIDE
of the line of the
test point.
If the inequality is
false, SHADE
THE
OPPOSITE SIDE
of the line of the
test point.
Graph the following inequality y < 3x ­ 1
Graph the inequality
y < 3x ­ 1
The point (­2,1) was chosen as the test point, because it can be clearly seen in the diagram.
[The easiest test point is usually (0,0)]
1 3(­2) ­ 1
1 ­6 ­1
1 ­7
false
(shade the opposite side of the line)
1. Graph y > 2x + 1
y intercept =
slope =
5
4
3
2
Solid or
1
dotted line?
­5 ­4 ­3 ­2 ­1
1 2 3 4 5
­1
­2
­3
­4
­5
Where do we shade?
2. y ≥ ½ x - 1
5
4
3
2
1
­5 ­4 ­3 ­2 ­1
1 2 3 4 5
­1
­2
­3
­4
­5
3. Graph y ≥3 ­ 3x
5
4
3
2
1
­5 ­4 ­3 ­2 ­1
1 2 3 4 5
­1
­2
­3
­4
­5
y ≥ 1/3x
5
4
3
2
1
­5 ­4 ­3 ­2 ­1
1 2 3 4 5
­1
­2
­3
­4
­5
4. 2y ­ 4 < 6x
5
4
3
2
1
­5 ­4 ­3 ­2 ­1
1 2 3 4 5
­1
­2
­3
­4
­5
5. 6x ­ 2y ≤ ­8
5
4
3
2
1
­5 ­4 ­3 ­2 ­1
1 2 3 4 5
­1
­2
­3
­4
­5