The document contains notes and examples about graphing linear inequalities on a coordinate plane. It discusses writing inequalities in y=mx+b form, determining the boundary line, and shading the appropriate region based on whether the inequality is <, ≤, >, or ≥. Key steps include solving the inequality for y, graphing the boundary line, and testing a point such as (0,0) to determine which side of the line to shade.

1. 3

2.  Notes
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3. Warm Up:
1. Solve the inequality: -1 <
𝟑 −𝟐𝒙
𝟓
< 3
4 > x and x > -6; write as one inequality -6 < x < 4
2. Solve for x: 1 -
𝟐
𝒙 −𝟐
1 +
𝟐
𝒙 −𝟐
Eliminate both denominators.
Hint: There are 2 terms in
both the numerator and the
denominator.
𝒙 − 𝟐 1 -
𝟐
𝒙 −𝟐
𝒙 − 𝟐 − 𝟐
𝒙 − 𝟐 + 𝟐
𝒙 − 𝟒
𝒙
A quick look at the 3rd quarter

4. Warm Up:
5. Graph the inequality: 2x + 3y > 12
x
y
2-2
(0,4)
(6,0)
3. Write an equation for a horizontal line
6. Write an equation for a line perpendicular to:
−𝟏
𝟑
x = 2y + 12.
4. Write an equation with an undefined slope

5. Recall…
Graph n < 3 on a number line.
-3 -2 -1 0 1 2 3 4

6. a. (4, 5); y < x + 1
Tell whether the ordered pair is a
solution of the inequality.
y < x + 1
Substitute (4, 5) for (x, y).
Substitute (1, 1) for (x, y).
b. (1, 1); y > x – 7
y > x – 7
5 4 + 1
5 5<
1 1 – 7
>1 –6
(4, 5) is not a solution. (1, 1) is a solution.
 

8. The boundary line also represents the related linear
equation....what is the related equation?
What is the
Inequality?
y > x + 4

9. Graphing Linear Inequalities
Step 1
Solve the inequality for y (solved EXACTLY
like an equation; slope-intercept form).
Step 2
Graph the solution (the boundary line).
Use a solid line for ≤ or ≥. Use a dashed
line for < or >.
Step 3
Shade the half-plane above the line for y >
or ≥. Shade the half-plane below the line for
y < or y ≤. Check your answer.

10. Graph y > 3 on the coordinate plane.
x
y

11. x
y
Graph x < -2 on the coordinate plane.

12. Graph y > -3x + 2 on the coordinate plane.
x
y
Boundary Line
y = -3x + 2
m = -3 b = 2
Test a point not on the line
test (0,0)
0 > -3(0) + 2
Not true!

13. Graph y -3x + 2 on the coordinate plane.
x
y

Instead of testing a point
If in y = mx + b form...
Shade
up
Shade
down
Solid
line
Dashed
line
 
> <
Graphing Linear Inequalities

14. Graph the solution of the linear inequality.
5x + 2y > –8
Step 1 Solve the inequality for y.
Step 2 Graph the boundary line and
Use a dashed line for >.
y =
−𝟓
𝟐
x – 4
Step 3: Test a point not on the
line. Use (0,0) when you can.
5(0) + 2(0) > -8, True or False?
If true, include that point in your
shading.

15. Graph the inequality.
3x - 4y > 12
-3x -3x
-4y > -3x + 12
-4 -4
y < x - 3
m = b = -3
Boundary Line
x
y
3
4
𝟑
𝟒
𝟑
𝟒

16. Problem
You have less than $5.00 in nickels and dimes,
find an inequality and sketch a graph to describe
how many of each coin you have.
Let n = # of nickels
Let d = # of dimes
0.05 n + 0.10 d < 5.00
or
5 n + 10 d < 500
Graphing Linear Inequalities

17. 5n + 10d < 500
n d
0 50
100 0
0 10 20 30 40 50 60 70 80 90 100
n
d
60
50
40
30
20
10
0

18. When dealing with angled lines,
If the inequality is > or > ,then you shade above
If the inequality is < or < ,then
you shade below
Finding a point not on the
line is still the safest and
surest method to determine
where to shade.

19. Graph y -3x + 2 on the coordinate plane.
x
y

Instead of testing a point
Arrange the equation in
y = mx + b form...
Shade
up
Shade
down
Solid
line
Dashed
line
 
> <
Graphing Linear Inequalities

20. Graph on the coordinate plane.
3x - 4y > 12
-3x -3x
-4y > -3x + 12
-4 -4
y < x - 3
3
4
m = b = -3
3
4
Boundary Line
x
y
Graphing Linear Inequalities

21. If the point makes the
inequality true, shade
that side of the line.
If the point does not
make the inequality true,
shade the opposite side of
the line.
Use (0,0) as a test if this
point is not on the line.

22. Quadrilateral ABCD has diagonals AC and BD.
Determine whether segment AC is perpendicular to BD
AC, m = 7
BD, m =
−𝟏
𝟕
The lines are perpendicular.