二元一次不等式表示的平面區(qū)域教學課件

問題1：下列方程的幾何意義是什么？①x+y–1=0方程的解集在平面直角坐標系中表示一條直線l。這條直線由無數(shù)多個點組成，其中點的坐標(x,y)是直線方程x+y－1=0的解。問題2：二元一次不等式的解集{(x,y)|x+y–1＞0}的幾何意義是什么呢？(Ⅱ)(Ⅰ)(Ⅲ)x二元一次不等式表示

的平面區(qū)域問題３：①在平面直角坐標系中畫出直線x=2.②直線x=2把整個平面分成幾個區(qū)域？你能畫出下列式子所表示的區(qū)域嗎？在平面直角坐標系中，所有的點被直線x+y-1=0分為幾類：3)在直線x+y-1=0左下方的平面區(qū)域內(nèi)。11x+y-1=0(Ⅱ)(Ⅰ)(Ⅲ)x2)在直線x+y-1=0右上方的平面區(qū)域內(nèi)；直線l可以看作是以二元一次方程x+y-1=0的解為坐標的點的集合{﹙x,y）︱x+y-1=0｝1)在直線x+y-1=0上;x+y-1=0⑵平面上任意一點P（x,y），代入x+y-1后得到的值會有幾種情況：yo⑶點P（x，y）在直線的哪一區(qū)域內(nèi)x+y-1的值大于0；等于0；小于0?⑴能否在直線外找一點P（x,y）,使得x+y-1=0？大于0；等于0；小于0如何證明你的判斷？思路一：在直線右上方任取一點(x,y)，過此點作一平行x軸的直線x+y-1=0０xyP0(x0,y0)(x,y)思路二：在直線右上方任取一點(x,y)，過此點作一平行y軸的直線x+y-1=0０xyP0(x0,y0)(x,y)X>x0,y=y0

x+y>x0+y0x+y-1>x0+y0-1=0X=x0,y>y0x+y>x0+y0x+y-1>x0+y0-1=0結(jié)論：一般地，二元一次不等式Ax+By+C>0在平面直角坐標系中表示直線Ax+By+C＝0某一側(cè)所有點組成的平面區(qū)域。我們把直線畫成虛線以表示區(qū)域不包含邊界直線。（同側(cè)同號）你有什么發(fā)現(xiàn)？

能不能猜想出y>kx+b表示的是直線y=kx+b的哪部分區(qū)域？同樣，y<kx+b表示的又是直線

y=kx+b的哪部分區(qū)域？結(jié)論１：y>kx+b表示直線上方的平面區(qū)域

y<kx+b表示直線下方的平面區(qū)域口訣：上大下小斜截式例題1：畫出下列不等式所表示的平面區(qū)域口訣：上大下小斜截式拓展引申共同探討：對于二元一次不等式Ax+By+C＞0（A、B不同時為0），如何確定其所表示的平面區(qū)域？結(jié)論2：當B>0時

Ax+By+C>0表示直線上方區(qū)域

Ax+By+C<0表示直線下方區(qū)域（注：由斜截式轉(zhuǎn)化為一般式進行研究探討或由一般式化歸為斜截式進行研究探討，并作比較）Ｐ７７．２．３強調(diào)：若B<0時則恰好結(jié)論相反;若B=0則最易判斷?？谠E：上正下負一般式（B>0）例題2:根據(jù)下列各圖中的平面區(qū)域用不等式表示出來（圖１包含y軸）6x+5y=22y=x-１1３－４Ｐ７８．５提出：采用“選點法”來確定二元一次不等式所表示的平面區(qū)域Ｐ７７．１強調(diào)：若直線不過原點，通常選（0，0）點;若直線過原點，通常選（1，0）、（-1，0）、（0，1）、(0,-1)等特殊點代入檢驗并判斷。_1。①二元一次不等式表示相應直線的某一側(cè)區(qū)域②口訣：上大下小斜截式上正下負一般式（B>0）小結(jié)2。畫二元一次不等式表示的平面區(qū)域的方法：可根據(jù)二元一次不等式與B的關(guān)系來確定

Ax+By+C>0與B的關(guān)系為:B>0時表示直線上方區(qū)域,B<0時表示直線下方區(qū)域。Ax+By+C<0

與B的關(guān)系為:B>0時表示直線下方區(qū)域,B<0時表示直線上方區(qū)域

思考題:不等式組

表示的又是怎樣的平面區(qū)域呢？初一英語第二學期同步串講第七講

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