(:title Inequality in 2 Variables - Graphing Region in Plane :) >>nav_bar<< %yel%Mathcasts         %exa%Examples      %pra%[[http://mathcasts.org/gg/enliven/af/lines/inequality2/inequality2_index.html|Practice]]%%    %mor%More      %up%[[glossary/L]] >><< [[<<]] >>&<< [table border=1 cellpadding=3 width=100%] [row] []>>&<< %ref b%Definition:%% A %red b%linear inequality in 2 variables%% is a [[GlossaryT/LinearEquation|linear equation]] in 2 variables in which the "=" has been replaced by an inequality. >>-<<%b reg%Regulation:%% The solution set of a linear inequality is a region in the plane bounded by the line of the corresponding linear equation. %dkr s8%(This set includes the points on the line only if inequality includes the equals sign, i.e. is '''not''' a strict inequality).%% >>-<<%b exa%Examples of linear inequalities in 2 variables:%% %exa%{$\bbox[border:1px #990000 dotted,1pt]{y>2x-3}$}%%  %bgr%{$\bbox[border:1px #990000 dotted,1pt]{2y+5x \leq 2}$}%%  %pra%{$\bbox[border:1px green dotted,1pt]{3s<2t-2}$}%% >>&<< [tableend] >>-<< [table border=1 cellpadding=3 width=825] [row] [](:showhide init=show div=div1 lshow="+" lhide="-":) InterActivity (:showhide init=hide div=div3 lshow="+" lhide="-":) %sol s9%Directions for InterActivity%% %newwin%%s9%[[http://mathcasts.org/gg/enliven/af/lines/inequality2/inequality2_index.html|Menu with 4 InterActivities (new window)]]%% (:div3 id=div3 class=s9 style="margin-left:20px" :) [table border=1 cellpadding=3 width=825] [row] []>>&<< (:html:)

Goal: Get familiar with the graph of a linear inequality in 2 variables - a region in the plane bounded by a solid or dashed line.

1. In the input box below, type or paste in a linear inequality in 2 variables x and y. Hit Enter and view the resulting region in the plane.
* You can type <= for  and  >= for .

(Samples: 3x+2y>=1, y>4x/5-11/5, 0.2x-0.5y≤2, ...)

2. To change the view, click on the Move tool and then click and drag the graph as desired.

• Note whether the line is solid or dashed depends on whether "equality" is included in the inequality.

3. Find the coordinates of any point in the shaded region and substitute its coordinates into the inequality. The inequality should be "true".

4. Find the coordinates of any point NOT in the shaded region and substitute its coordinates into the inequality. The inequality should be "false".

• To start over, enter a new inequality and hit Enter.

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Linear Inequality:
 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Many thanks to mathmagic and piman!      LFS , Created with GeoGebra
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 Linear Inequality 1: Linear Inequality 2: Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
(:htmlend:) (:ifend:) (:div1end :) [tableend] >>-<< ---- >>&<< %rel%Related Topics *[[Lines]] *[[GlossaryT/Slope|Slope of a Line]] *[[GlossaryT/Systems2|Systems of Linear Equations 2x2]] *[[GlossaryT/LinearFunction|Linear Functions]] *[[GlossaryT/LinearEquation|Linear Equations]] *[[Cartcoor2|Cartesian Coordinates - Points in the Plane]] >>-<< [table border=1 cellpadding=3 width=100%] [row] []>>&<<(:showhide init=hide div=div9 lshow="+" lhide="-":) Metadata (:div9 id=div9 :) [table class=column border=1 width=100% cellpadding=3] [row] [ width=110px] Global []Graphing Linear Inequalities in 2 Variables [row] []Brief []InterActivity for graphing 1 or 2 linear inequalities in 2 variables [row] []Grade []8th and up (must know how to graph lines) [row] []Strand []Algebra 1 - 2 [[http://math247.pbwiki.com/Algebra+with+GeoGebra| AF at Math247]] [row] []Standard []%popwin%[[Standards/Is1al2-2?action=popopen|Algebra 1 2.2]]   %popwin%[[Standards/ca2al2?action=popopen|CA Algebra 2 2.0]]   %popwin%[[standards/ACTgr28?action=popopen|ACT GR 28-32]]   %popwin%[[standards/ACTgr33?action=popopen|ACT GR 33-36]] [row] []Keywords []linear, inequality, system, 2 variables, algebra, dynamic, freeware, applet, offline, online [row] []Comments []Hopefully a reverse inactivity coming soon. [row] []Credits []David Cox for asking; MathMagic and Piman of the GeoGebra forum for creating the algorithm! [row] []Download |[]Zip Attach:zip.gif - [[http://mathcasts.org/gg/enliven/af/lines/inequality2/inequality2_offline.zip|Completely Offline]] & [[http://mathcasts.org/gg/enliven/af/lines/inequality2/inequality2_school.zip|School]] [row] []Author []LFS - [[mailto:emath@emathforall.com?subject=ggb_problems|contact]] [row] []Type []Freeware - Available for Offline and Online Use - Translatable (html) [row] []Use []Requires [[http://www.java.com/en/download/index.jsp|sunJava player]] [tableend] (:div9end:) [tableend] >>&<< ---- >>&<< [table width=100%] [row] [][[Glossary/S| Attach:main/tri_purple_up_a.gif ]] [[Glossary/S| Up one level]] [r](:html:) (:htmlend:) [tableend] (:div7111 id=div7111 :) (:div7111end :) (:div7112 id=div7112 :) (:div7112end :) (:div7113 id=div7113 :) (:div7113end :)