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Here are some tips for Graphs to Linear Inequalities, which aligns with Florida 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 ? -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 = -54 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 ?
 -54 x + 3
0 ?
 -54 (5) + 3
Plug in (5, 0)
0 >
 -134
"Greater than" to make the inequality true
y
 -54 x + 3
Boundary line is solid

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