7/31/2019 2D Inequalty Graphs

1/14

7/31/2019 2D Inequalty Graphs

2/14

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.

A. The equation of each line is y = x + 3.

B. The lines in each graph are the same and represent all of

the solutions to the equation y = x + 3.

C. The graph on the right is shaded above the line and thismeans that all of these oints are solutions as well.

7/31/2019 2D Inequalty Graphs

3/14

Pick a point from the shadedregion and test that point in

the equation y = x + 3.

Point: (-4, 5)

y x 3

5 4 3

5 1

This is incorrect. Five

is greater than or equalto negative 1.

5 1

5 1 5 1or

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 > -1.

The area above the line is shaded.

7/31/2019 2D Inequalty Graphs

4/14

7/31/2019 2D Inequalty Graphs

5/14

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

().

4. Pick a point above the line or below the line. Test that point in

the inequality. If it makes the inequality true or not true, then

shade accordingly what the question asks (i.e. leave unshaded

or shade the region showing the inequality).

5. Systems of inequalitiesFollow 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.

7/31/2019 2D Inequalty Graphs

6/14

Graph the following linear system of inequalities.

y x

y x

2 4

3 2

x

y

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.

7/31/2019 2D Inequalty Graphs

7/14

Graph the following linear system of inequalities.

y x

y x

2 4

3 2y x2 4 Point (0,0)

0 2(0) - 4

0 -4

The region above the lineshould be shaded.

x

y

Now do the same for the

second inequality.

7/31/2019 2D Inequalty Graphs

8/14

Graph the following linear system of inequalities.

y x

y x

2 4

3 2

x

y

Use the slope and y-intercept to plot two

points for the second

inequality.

Draw in the line. For