By: Andrea Bruno & William Wade

The Basics Practice Problems

Above & Beyond Links For More Help and Games

Just Click the Picture to go to that section

Graphing Inequalities

The basics of graphing Inequalities in two variables is graphing an open sentence that has: <, >, ≤, or ≥. < : less than, dotted line on graph > : greater than, also a dotted line on graph ≤ : less than or equal to, solid line on graph ≥ : greater than or equal to, also a solid

line on graph

Graphing Inequalities

The equation for graphing inequalities is

y > mx + b b is the y-intercept and m is the slope of the line. The slope begins on the y-intercept

Remember RISE over RUN

Notice the dotted line!

The 4 is the 1st point on the y-intercept. The 2/1 is the slope going up 2 and over 1

Example 1

Shading Part of solving inequalities is shading the solution If the inequality is greater than or greater than or equal to you shade

above the line Less than or less than or equal to you shade below the line The solution is where both shadings meet

Example 21. After graphing the two

inequalities you must shade (color)

2. Since the first (green) inequality is ≥ the line is solid and is shaded on top

…with the other one the line is dotted and is also shaded on top

Converting Inequalities

Sometimes the inequality has a number with the y. When this happens the problem must be converted back to slope

intercept form ( y>mx+b )

: 2y>2x+4Step 1: divide both sides by 2 (to get the y by itself)Step 2: write out the final equation (y>x+2)Step 3: Graph ~ 2 is the y intercept so put your first point on the y axisStep 3a: your slope is 1 or in fraction form 1/1

When multiplying or dividing with a negative number the sign of the inequality is flipped. For example: -y<x+9 would equal: y>-x-9 in slope intercept form

Notice the dotted line!!

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Example 3

Practice Problems

1. 2y<8x-1

2. Y>-7x+5

3. 5y≤2x-3 & 2y>-5x+6

4. y≥-4x+8 & y<-5x+6

5. -y<x-4 & y≥-x+7

6. 17-x<y & 3y≤15x+1

7. -6+9x≥3y & 3y>-9x+6

8. 9-3x≤y & 2y≥9x+3

9. -18+5x>-2y & y>8+5x

10. 1-10x<y & y≥3x-7

Click the Equation to find out the Answers

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Graphing advanced inequalities is no different from normal inequalities Just use 3 or more lines Create different polygons Also, find the area of those polygons

If you don’t understand the Basic section, Do Not continue the Above & Beyond section

• The following inequalities were graphed:Y<4x -1Y>-2.5x+3Y≤0.5x -1• The Area where green, red, and blue are combined is the solution

• When you have 4 inequalities and is good enough to make a rectangle you can also find the area of that rectangle!!

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Links For More Help

http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_05/study_guide/pdfs/alg1_pssg_G051.pdf

http://www.purplemath.com/modules/ineqgrph.htm

http://www.math-play.com/Inequality-Game.html

http://www.mathwarehouse.com/quadratic-inequality/how-to-solve-and-graph-quadratic-inequality.php

http://www.sparknotes.com/math/algebra2/inequalities/section1.html

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Summary Tool

≤Less Than or

Equal to

≥Greater than or

equal to

>Greater than

<Less than

When multiplying or dividing with a negative number the sign of the inequality is flipped

The solution is where both shadings meet

Remember RISE over RUN

Answer #1

4x-.5 is the simplified form of 2y<8x-1

Remember the dotted line

Also shaded below because the inequality is <

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Answer #2

Remember the line is dotted

Also shaded above because the inequality is >

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Answer #3

Watch the lines! Shaded below on ≤

and above on >

≤

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Answer #4

Remember the line

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Answer #5

Be sure to locate your solution Correctly

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Answer #6 Back to Index

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Answer #7 Back to Index

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Answer #8 Back to Index

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Answer #9

Check your graphs See the dotted lines!

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Back to Practice Problems Sorry about the graph but you should still know the area of the solution

Answer #10 Back to Index

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The inequalities are written in simplified form