Graphing

1
Graphing Systems of Inequalities
2
Look at the two graphs. Determine the
following A. The equation of each line. B. How
the graphs are similar. C. How the graphs are
different.

1. The equation of each line is y x 3.
2. The lines in each graph are the same and
   represent all of the solutions to the equation y
   x 3.
3. The graph on the right is shaded above the line
   and this means that all of these points are
   solutions as well.

3
Inequalities with Greater Than
Point (-4, 5)
Pick a point from the shaded region and test that
point in the equation y x 3.
This is incorrect. Five is greater than or equal
to negative 1.
If a solid line is used, then the equation would
be 5 ? -1. If a dashed line is used, then the
equation would be 5 gt -1. The area above the line
is shaded.
4
Inequalities with Less Than
Point (1, -3)
Pick a point from the shaded region and test that
point in the equation y -x 4.
This is incorrect. Negative three is less than
or equal to 3.
If a solid line is used, then the equation would
be -3 ? 3. If a dashed line is used, then the
equation would be -3 lt 3. The area below the line
is shaded.
5
Graphing Linear Inequalities

1. Write the inequality in slope-intercept form.
2. Use the slope and y-intercept to plot two points.
3. Draw in the line. Use a solid line for less than
   or equal to (?) or greater than or equal to (?).
   Use a dashed line for less than (lt) or greater
   than (gt).
4. Pick a point above the line or below the line.
   Test that point in the inequality. If it makes
   the inequality true, then shade the region that
   contains that point. If the point does not make
   the inequality true, shade the region on the
   other side of the line.
5. Systems of inequalities Follow steps 1-4 for
   each inequality. Find the region where the
   solutions to the two inequalities would overlap
   and this is the region that should be shaded.

6
Example
Graph the following linear system of inequalities.
Use the slope and y-intercept to plot two points
for the first inequality.
Draw in the line. For ? use a solid line.
Pick a point and test it in the inequality.
Shade the appropriate region.
7
Example
Graph the following linear system of inequalities.
The region above the line should be shaded.
Now do the same for the second inequality.
8
Example
Graph the following linear system of inequalities.
Use the slope and y-intercept to plot two points
for the second inequality.
Draw in the line. For lt use a dashed line.
Pick a point and test it in the inequality.
Shade the appropriate region.
9
Example
Graph the following linear system of inequalities.
The region below the line should be shaded.
10
Example
Graph the following linear system of inequalities.
The solution to this system of inequalities is
the region where the solutions to each inequality
overlap. This is the region above or to the left
of the green line and below or to the left of the
blue line. Shade in that region.
11
You Try One!

• Graph the following linear systems of
  inequalities.
• y gt x 4
• y gt x 2

12
Problem 1
Use the slope and y-intercept to plot two points
for the first inequality.
Draw in the line.
Shade in the appropriate region.
13
Problem 1
Use the slope and y-intercept to plot two points
for the second inequality.
Draw in the line.
Shade in the appropriate region.
14
Problem 1
The final solution is the region where the two
shaded areas overlap (purple region).