INTRO

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Graphing a linear inequality can be broken down into two major parts:

- graphing a line
- and shading the area that agrees with the linear inequality.

$y$

$x$

Line: $y<0$

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.

CALCULATOR

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## Graphing Linear Inequalities Calculator

KEY STEPS

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## How to Graph Linear Inequalities

### Step 1. Isolate the $y$.

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

$x$

$=$$0$

).### Step 3. Find another point on the line.

We can use the slope or plug in another

$x$-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 asolid line.
- If the boundary itself is not safe ($>$ or $<$), we use adotted line.

### Step 5. Shade the correct area.

- If $y$ $>$ $mx+b$ or $y$ $≥$ $mx+b$, then everything greater than the line is safe, and we shade above.
- If $y$ $<$ $mx+b$ or $y$ $≤$ $mx+b$, 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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