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	?	-1	Plug in (-3,0)
-3	<	-1	"Less than" makes the inequality true
x	<	-1	Boundary 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

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