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在六年制重点中学高中数学课本(平面)《解析几何》中,增:选了“二元一次不等式表示的区域”(下文称“区域”)一节。这一节在定义了直线y=kx+b把平面分为上半平面和下半平面后,已经给出了两种判断“区域”的方法:一种是,选点代入不等式的判断法;另一种是,以y的系数B为依据,结合不等号的方向进行分析推断的方法。在教学实践中看到,学生在掌握运用后一种方法时,对抛开x的系数,仅依据y的系数B进行分析判断,有人感到不习惯。为此,笔者抛砖引玉,另外给出了一种“区域”的判断方法。
In the six-year key middle school mathematics textbook (planar) Analytic Geometry, Gain: selected the section “Region of Binary Inequalities” (hereinafter referred to as “region”). In this section, after defining the straight line y=kx+b to divide the plane into an upper half plane and a lower half plane, two methods for judging “region” have been given: One is the method of substituting the selected point into inequality; The other is based on the coefficient B of y, and the method of analysis and inference is combined with the direction of inequality. In the teaching practice, when students master the use of the latter method, they will analyze and judge only the coefficient y of y on the coefficient of x, and some people feel unfamiliar. To this end, the author throws bricks to the surface, and also gives a “zone” judgment method.