Graphing Inequalities Notes

How to Determine

the Type of Line to Draw

Inequality

Symbol

Type of Line

> or <

Dotted Line

> or <

Solid Line

Choose the type of line
for the inequality given.

1. y > 3x - 2

a. Solid

b. Dotted

2. y > ¼x - 5

a. Solid

b. Dotted

Choose the inequality symbol for the
line shown.

< or >

Choose the inequality symbol for the
line shown.

< or >

If the

inequality is:

Shade

y > mx + b

or

y > mx + b

Above the

line

y < mx + b

or

y < mx + b

Below the line

x

y

Graph y > x - 2.

1. Graph
the line

y = x - 2.

2. Since y >, shade
above the line.

x

y

Graph y < x - 2.

1. Graph
the line

y = x - 2.

2. Since y <, shade
below the line.

Do you do
anything
different when
the line is dotted
rather than
solid?

LessonStart

Lesson
Start

LessonStart

Lesson
Start

x

y

Graph y > x - 2.

2. Since y >, shade
above the line.

1. Graph
the line

y = x - 2,
but make
the line
dotted.

x

y

Graph y < x - 2.

1. Graph
the line

y = x - 2,
but make
the line
dotted.

2. Since y <, shade
below the line.

x

y

Graph y > -½x + 3

Type of
line:

Solid

Dotted

Dotted

x

y

Graph y > -½x + 3

Type of
line:

Solid

Dotted

Shade ___ the line.

Above

Above

Below

LessonStart

Lesson
Start

x

y

Graph y > -½x + 3

Type of
line:

Solid

Dotted

Shade ___ the line.

Above

Below

x

y

Choose the correct inequality for the graph shown.

y < 1/3 x + 2

y < 1/3 x + 2

y > 1/3 x + 2

y > 1/3 x + 2

Where to Shade for Undefined or
No Slopes:

The inequality must be in

x # (no y)

format.

can be:

>, >, <, or <.

If the

inequality is:

Shade
To the

x > #

or

x > #

Right of the

line

x < #

or

x < #

Left of the line

x

y

Graph x > -2

1. Draw
a dotted
vertical
line at x
= -2.

2. Shade to
the right of
the line.

x

y

Graph x < -2.

1. Graph
the line

X = -2.

2. Shade
to the left
of the line.

x

y

Graph x > 3.

Choose type of
line.

Solid

Solid

Dotted

x

y

Graph x > 3.

Choose type of
line.

Solid

Choose
where to
shade.

Left

Right

Right

x

y

Graph x > 3.

Choose type of
line.

Solid

Choose
where to
shade.

Right

Solve -3x - 2y < 12.

+3x

+3x

-2y < 3x + 12

-2 -2

-2

y < -3/2 x - 6
>

Choose the correct inequality.

1. 2x + 5y > -10

y > -2/5 x - 2
y < -2/5 x - 2

y > 2/5 x + 2
y < 2/5 x + 2

2. 3x - 2y > 10

y > -2/3 x - 5
y < -2/3 x - 5

y > 2/3 x - 5
y < 2/3 x - 5

Example 1

⚫
Which ordered pair is a solution of

5x - 2y ≤ 6?

A. (0, -3)
B. (5, 5)
C. (1, -2)
D. (3, 3)

Example 2

⚫ Graph the inequality x ≤ 4 in a coordinate

plane.

⚫ Decide whether to
use a solid or
dashed line.

⚫ Use (0, 0) as a
test point.

⚫ Shade where the
solutions will be.

y

x

5

5

-5

-5

Example 3

⚫ Graph 3x - 4y > 12 in a coordinate plane.

⚫ Sketch the boundary line of the graph.

▪ Solve for “y” first:
▪ y < ¾x - 3

⚫ Solid or dashed
line?

⚫ Use (0, 0) as a
test point.

⚫ Shade where the
solutions are.

y

x

5

5

-5

-5

Example 4:

⚫ Graph y < 2/5x in a coordinate plane.
• What is the slope and y-intercept?
• m = 2/5
• b = (0,0)
• Solid or dashed
line?

⚫ Use a test point
OTHER than the

origin.

⚫ Shade where the
solutions are.

y

x

5

5

-5

-5

Graph: y ≥

-

3/2x + 1

Step 1: graph
the boundary
(the line is
solid ≥)

Step 2: test
a point NOT
On the line
(0,0) is always
The easiest if it’s
Not on the line!!
3(0) + 2(0) ≥ 2
0 ≥ 2
Not a solution

So shade the other side of the line!!

Graph: y <

6

Graph: 4x

–

2y < 7