by: andrea bruno & william wade. the basicspractice problems above & beyondlinks for more...
TRANSCRIPT
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!!
Back to Index
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
Back to Index
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!!
Back to Index
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
Back to Index
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 <
Back to Index
Back to Practice Problems
Answer #2
Remember the line is dotted
Also shaded above because the inequality is >
Back to Index
Back to Practice Problems
Answer #3
Watch the lines! Shaded below on ≤
and above on >
≤
Back to Index
Back to Practice Problems
Answer #4
Remember the line
Back to Index
Back to Practice Problems
Answer #5
Be sure to locate your solution Correctly
Back to Index
Back to Practice Problems
Answer #6 Back to Index
Back to Practice Problems
Answer #7 Back to Index
Back to Practice Problems
Answer #8 Back to Index
Back to Practice Problems
Answer #9
Check your graphs See the dotted lines!
Back to Index
Back to Practice Problems Sorry about the graph but you should still know the area of the solution
Answer #10 Back to Index
Back to Practice Problems
The inequalities are written in simplified form