QUICK LINKS


Introduction

QUICK LINKS


Introduction

Graphing Linear Inequalities

INTRO
Graphing a linear inequality can be broken down into two major parts:
  1. graphing a line
  2. and shading the area that agrees with the linear inequality.
If we imagine that the graph has a safety zone and a danger zone, the line represents the boundary between the two zones, and the shaded area represents the safety zone (where we want to be).
Line:
Select the safe Brains:

Depending on the type of inequality, the boundary/line can be a part of either the safety or danger zone.

If we have , then the boundary is safe, and we use a solid line.
The inequality symbol also tells us which side of the line we need to shade in. When , everything greater than the line is safe, and we shade the area above.

Graphing Inequalities with Horizontal Boundaries

If our inequality is in the form , where is a number:
  • The boundary will be a
    horizontal, dotted line
    that cuts through all the points where .
  • We shade the
    area above
    .

Graphing Inequalities with Vertical Boundaries

If our inequality is in the form , where is a number:
  • The boundary will be a
    vertical, dotted line
    that cuts through all the points where .
  • We shade the
    area to the right
    .
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to graph linear inequalities and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

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CALCULATOR

Graphing Linear Inequalities Calculator

Step 1. Isolate the .

Step 4. Connect the two points using the right type of line.

The line is like the boundary between the safety zone and the danger zone.
Because the boundary itself is not safe (
or
), we use a
dotted line
.

Step 5. Shade the correct area.

If or , then everything less than the line is safe, and we shade below.
If or , then everything less than the line is safe, and we shade to the left.
KEY STEPS

How to Graph Linear Inequalities

Step 1. Isolate the .

Remember, if we divide by a negative number, we need to flip the inequality symbol.

Step 2. Find one point on the line.

We can treat the inequality like an equation to find points on the line.
We find it easiest to start by finding the y-intercept (where
).

Step 3. Find another point on the line.

We can use the slope or plug in another
-value
to move to another point.

Step 4. Connect the two points using the right type of line.

The line is like the boundary between the safety zone and the danger zone.
  • If the boundary itself is safe (
    or
    ), we use a
    solid line
    .
  • If the boundary itself is not safe (
    or
    ), we use a
    dotted line
    .

Step 5. Shade the correct area.

  • If or , then everything greater than the line is safe, and we shade above.
  • If or , then everything less than the line is safe, and we shade below.
LESSON
Graphing Linear Inequalities
PRACTICE
Graphing Linear Inequalities
CONCLUSION
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