Download 6.5 Graphing Linear Inequalities in Two Variables

6.5 Graphing
Linear
Inequalities in
Two Variables
Wow, graphing
really is fun!
Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.FIF.C.7, HS.F-LE.A.2): The student will understand that linear relationships
can be described using multiple representations.
4
3
2
1
0
In addition to
level 3.0 and
above and
beyond what
was taught in
class, the
student may:
· Make
connection with
other concepts
in math
· Make
connection with
other content
areas.
The student will
understand that linear
relationships can be
described using multiple
representations.
- Represent and solve
equations and
inequalities graphically.
- Write equations in
slope-intercept form,
point-slope form, and
standard form.
- Graph linear equations
and inequalities in two
variables.
- Find x- and yintercepts.
The student
will be able to:
- Calculate
slope.
- Determine if
a point is a
solution to an
equation.
- Graph an
equation using
a table and
slope-intercept
form.
With help
from the
teacher, the
student has
partial
success with
calculating
slope, writing
an equation
in slopeintercept
form, and
graphing an
equation.
Even with help,
the student
has no
success
understanding
the concept of
a linear
relationships.
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.
Use x- and yintercepts:
(0, 6) & (5, 0)
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.
Use x- and yintercepts:
(0, -1) & (1/2, 0)
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