Graphical Inequalities

This lesson covers:

  1. How to show inequalities on a graph
  2. How to find the region on a graph that satisfies multiple inequalities. 

When sketching inequalities with < or > signs, such as x < 3, should we use dashed or solid lines?

Solid

Dashed

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When sketching inequalities with ≤ or ≥ signs, such as y ≥ -6, should we use dashed or solid lines?

Solid

Dashed

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Which line on the graph below represents the inequality:

x<5
Graph showing lines A B and C representing different inequalities with arrows indicating directions.

C

B

A

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Which line on the graph below represents the inequality:

y≤4
Graph showing three lines labeled A, B, and C, representing different inequalities.

A

C

B

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Write the inequality that represents the line on the graph below.

Graph showing a vertical line on a coordinate grid representing a linear inequality.
x\leq-1|x\text{ \leq}-1|x\text{ \leq}-1|x\text{\leq}-1|x\le-1|x\text{\leq}-1|x≤-1

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Write the inequality that represents the line on the graph below.

Graph showing a dashed line representing an inequality with arrows pointing downwards.
y<-3

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Write the inequality that represents the line on the graph below.

(Tip: Find the equation of the line first)

Graph showing a dashed line with positive slope and inequality arrows.
y>x-1|y>1x-1

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Sketch a graph similar to the one below and shade the region that satisfies all three of these inequalities:


y > -4,   x ≤ 5,   y < 2x + 2

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