Math Practice Online: MathScore.com

Math Practice Online > free > lessons > Minnesota > 9th grade > Graphs to Linear Inequalities

If your child needs math practice, click here.

For sample problems, click here.
Here are some tips for Graphs to Linear Inequalities, which aligns with Minnesota state standards:

Graphs to Linear Inequalities


For this topic, you need to know how to find the equation of a line.
To review the Graphs to Linear Equations topic, see here.

In this topic, you will find the inequality based on its graph.

To find the ineqaulity, follow these steps:

  1. Find the equation of the boundary line.
  2. Choose a point (x, y) on the shaded side of the line.
  3. Plug x and y into the bounday line equation to determine the inequality sign.
    1. If the boundary line is solid, then the inequality sign is either ≥ or ≤.
    2. If the boundary line is dotted, then the inequality sign is either > or <.


Example 1:

Write the inequality that represents this graph. Examples: y>3x/4, x<=2, y>=1, y>-2x
Inequality:
Step 1: Find the equation of the boundary line.
The boundary line is vertical. Its equation is x = -1.

Step 2: Choose a point (x, y) on the shaded side of the line.
Let's pick (-3, 0) on the shaded side.

Step 3: Plug x and y into the bounday line equation to determine the inequality sign.
x?-1
-3?-1Plug in (-3,0)
-3<-1"Less than" makes the inequality true
x<-1Boundary line is dashed


Example 2:

Write the inequality in y=mx+b format. Examples: y>2x-3, y<=-4x/3+1
Inequality:
Step 1: Find the equation of the boundary line.
The slope of the line is -5/4 and the y-intercept is 3.
So the equation of the boundary line is y = -5
4
x + 3.

Step 2: Choose a point (x, y) on the shaded side of the line.
Let's pick (5, 0) on the shaded side.

Step 3: Plug x and y into the bounday line equation to determine the inequality sign.
y ?
-5
4
x + 3
0 ?
-5
4
(5) + 3
Plug in (5, 0)
0 >
-13
4
"Greater than" to make the inequality true
y
-5
4
x + 3
Boundary line is solid

Copyright Accurate Learning Systems Corporation 2008.
MathScore is a registered trademark.