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WARM UP
GRAPH THE INEQUALITY (Lesson 1.4)
1. x < 2
2. y > 5
3. x – 2 > 3
4. 2y < 6
4
WARM UP
GRAPH THE INEQUALITY (Lesson 1.4)
1. x < 2
2. y > 5
3. x – 2 > 3
4. 2y < 6
3
WARM UP
GRAPH THE INEQUALITY (Lesson 1.4)
1. x < 2
2. y > 5
3. x – 2 > 3
4. 2y < 6
2
WARM UP
GRAPH THE INEQUALITY (Lesson 1.4)
1. x < 2
2. y > 5
3. x – 2 > 3
4. 2y < 6
1
WARM UP
GRAPH THE INEQUALITY (Lesson 1.4)
1. x < 2
2. y > 5
3. x – 2 > 3
4. 2y < 6
0
Pre-Lesson to 7.6 Systems of Linear
Inequalities
The graph of a linear
inequality in two variables is
the graph of the solutions of
the inequality.
The graph of 2x – 3y ≥ -2 is
shown at the right.
The graph includes the line
2x -3y = -2 and the shaded
region below the line.
Pre-Lesson to 7.6 Systems of Linear
Inequalities
Every point that is on the line
or in the SHADED half-plane
is a solution of the inequality.
Every other point in the plane
is not a solution.
Pre-Lesson to 7.6 Systems of Linear
Inequalities
Graphing a Linear Inequality
① Graph the corresponding equation.
Use a dashed line for < or >. Use a solid
line for < or > .
② Test the coordinates of a point (the
origin) in one of the half-planes.
③ Shade the half-plane containing the
point if it is a solution of the inequality. If
it is not a solution, shade the other halfplane.
Pre-Lesson to 7.6 Systems of Linear
Inequalities
EXAMPLE 1 Vertical Lines
Graph the inequality x < -2
SOLUTION
① Graph the
corresponding equation
x = -2. The graph of x = -2
is a vertical line. The
inequality is <, so use a
dashed line.
Pre-Lesson to 7.6 Systems of Linear
Inequalities
EXAMPLE 1Vertical
Lines
Graph the inequality x < -2
SOLUTION
② Test a point. The origin
(0, 0) is not a solution and
it lies to the right of the
line. So all the points to
the left are solutions.
(0, 0)
Pre-Lesson to 7.6 Systems of Linear
Inequalities
EXAMPLE 1
Vertical Lines
Graph the inequality x < -2
SOLUTION
③ Shade the half-plane to
the left of the line.
Pre-Lesson to 7.6 Systems of Linear
Inequalities
EXAMPLE 2 Horizontal Lines
Graph the inequality y < 1
SOLUTION
① Graph the
corresponding equation
y = 1. The graph of y = 1 is
a horizontal line. The
inequality < is used, so use
a solid line.
Pre-Lesson to 7.6 Systems of Linear
Inequalities
EXAMPLE 2 Horizontal Lines
Graph the inequality y < 1
SOLUTION
② Test a point. The origin
(0, 0) is a solution and it
lies below line. So the
graph of y < 1 is all points
below the line y = 1.
(0, 0)
Pre-Lesson to 7.6 Systems of Linear
Inequalities
EXAMPLE 2 Horizontal Lines
Graph the inequality y < 1
SOLUTION
③ Shade the half-plane
below the line.
Pre-Lesson to 7.6 Systems of Linear
Inequalities
SUMMARY
> (greater than) Dashed line, shade above.
< (less than) Dashed line, shade below.
> (greater
than or equal to) Solid line, shade
CERTIFIED
above.
< (less than or equal to) Solid line, shade
below.