Section 2.7 Lecture Notes
Objectives:
• Graph linear inequalities
• Graph absolute value inequalities
GRAPHING LINEAR INEQUALITIES
The line formed by the equation y=mx+b forms the boundary where the x and y
coordinates of the ordered pair make each side of the problem equal.
There are many different pairs of x and y that would satisfy the inequality so we show
the answer by shading the region on the graph that contains the ordered pairs that will
satisfy the inequality.
≤ or ≥ is a solid boundary line
< or > is a dashed boundary line
Example: Graph y ≤ 2 x + 1
STEPS:
1. Determine if the boundary line will be
solid or dashed.
2. Graph the boundary line.
3. Plug in (0, 0) for the x and y
4. If (0, 0) satisfies the inequality shade that
side of the boundary line.
5. If (0, 0) does not satisfy the inequality,
shade the other side of the boundary line.
GRAPHING ABSOLUTE VALUE INEQUALITIES
Graph the absolute value boundary line as if it were an absolute value equation. Then
follow the same steps as linear inequalities.
Example: Graph y > x + 2
STEPS:
1. Determine if the boundary line will be
solid or dashed.
2. Graph the boundary “V”.
3. Plug in (0, 0) for the x and y
4. If (0, 0) satisfies the inequality shade that
side of the boundary line.
5. If (0, 0) does not satisfy the inequality,
shade the other side of the boundary line.
Practice Problems:
1. y < x − 2
2. y + 2 ≥ 3x
3. y < x − 2 − 3
4.
y+ x <2