Download 6.5 Graphing Linear Inequalities in Two Variables

6.5 Graphing
Linear
Inequalities in
Two Variables
Wow, graphing
really is fun!
What is a linear inequality?
• A linear inequality in x and y
is an inequality that can be
written in one of the
following forms.
• ax + by < c
• ax + by ≤ c
• ax + by > c
• ax + by ≥ c
• An ordered pair (a, b) is a solution of a
linear equation in x and y if the
inequality is TRUE when a and b are
substituted for x and y, respectively.
• For example: is (1, 3) a solution of
4x – y < 2?
• 4(1) – 3 < 2
• 1 < 2 This is a true statement so (1, 3)
is a solution.
Check whether the ordered pairs are
solutions of 2x - 3y ≥ -2.
a. (0, 0)
b. (0, 1) c. (2, -1)
(x, y) Substitute
A (0,0) 2(0) – 3(0)
B (0,1) 2(0) – 3(1)
C (2,-1) 2(2) – 3(-1)
Conclusion
= 0 ≥ -2 (0,0) is a
solution.
= -3 ≥-2 (0, 1) is NOT
a solution.
= 7 ≥ -2 (2, -1) is a
solution.
Graph the inequality 2x – 3y ≥ -2
3
2
1
-3 -2 -1
-1
-2
-3
1 2 3 4
Every point in the
shaded region is a
solution of the
inequality and
every other point is
not a solution.
Steps to graphing a
linear inequality:
1. Sketch the graph of the
corresponding linear
equation.
1. Use a dashed line for
inequalities with < or >.
2. Use a solid line for inequalities
with ≤ or ≥.
3. This separates the coordinate
plane into two half planes.
2. Test a point in one of the
half planes to find
whether it is a solution of
the inequality.
3. If the test point is a
solution, shade its half
plane. If not shade the
other half plane.
Sketch the graph of
6x + 5y ≥ 30
1.
Write in slopeintercept form:
y ≥ -6/5x + 6
This will be a solid line.
2. Test a point. (0,0)
6(0) + 5(0) ≥ 30
0 ≥ 30 Not a solution.
3. Shade the side that
doesn’t include (0,0).
6
4
2
-6 -4 -2
-2
-4
-6
2 4 6 8
Sketch the graph y < 6.
1.
This will be a
dashed line at
y = 6.
2. Test a point. (0,0)
0 < 6 This is a
solution.
3. Shade the side
that includes (0,0).
6
4
2
-6 -4 -2
-2
-4
-6
2 4 6 8
Sketch the graph of 2x – y ≥ 1
1.
Write in slopeintercept form:
y = 2x – 1
This will be a solid line.
2. Test a point. (0,0)
2(0) - 0 ≥ 1
0 ≥ 1 Not a solution.
3. Shade the side that
doesn’t include (0,0).
3
2
1
-3 -2 -1
-1
-2
-3
1 2 3 4