Download 2 Vertical Lines 3 Horizontal Lines

GRAPHING A LINEAR INEQUALITY
Student Help
STUDY TIP
A dashed line indicates
that the points on the
line are not solutions.
A solid line indicates
that the points on the
line are solutions.
STEP
Graph the corresponding equation. Use a dashed line for
> or <. Use a solid line for ≤ or ≥.
STEP
Test the coordinates of a point in one of the half-planes.
STEP
Shade the half-plane containing the point if it is a solution
of the inequality. If it is not a solution, shade the other
half-plane.
EXAMPLE
2
Vertical Lines
Graph the inequality x < 2.
y
Solution
3
Graph the corresponding equation x 2.
The graph of x 2 is a vertical line. The
inequality is <, so use a dashed line.
Student Help
x < 2
3
Test a point. The origin (0, 0) is not a
STUDY TIP
You can use any point
that is not on the line
as a test point. It is
convenient to use the
origin because 0 is
substituted for each
variable.
1
1 (0, 0)
1
3
x
3
x
3
solution and it lies to the right of the line.
So the graph of x < 2 is all points to the
left of the line x 2.
Shade the half-plane to the left of the line.
ANSWER 䊳
The graph of x < 2 is the half-plane to the left of the graph
of x 2. Check by testing any point to the left of the line.
EXAMPLE
3
Horizontal Lines
Graph the inequality y ≤ 1.
y
Solution
3
Graph the corresponding equation y 1.
The graph of y 1 is a horizontal line. The
inequality is ≤, so use a solid line.
3
Test a point. The origin (0, 0) is a solution
y≤1
and it lies below the line. So the graph of
y ≤ 1 is all points on or below the line y 1.
1 (0, 0)
1
3
Shade the half-plane below the line.
ANSWER 䊳
The graph of y ≤ 1 is the graph of y 1 and the half-plane below
the graph of y 1. Check by testing any point below the line.
Horizontal and Vertical Lines
Graph the inequality.
1. x ≥ 1
368
Chapter 6
2. x < 4
Solving and Graphing Linear Inequalities
3. y > 3
4. y ≤ 2