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一部分同学在求直线方程时,由于对直线方程几种形式适用范围认识不清,有的是做题方法不当.经常会出现“漏解”现象.现举几例,进行剖析,希望大家从中汲取教训、澄清概念. 1.使用直线方程的截距式常导致漏解例1 求过点P(2,3),并且在两坐标轴上的截距相等的直线方程. 错解:设所求直线方程为x/a+y/b=1. 依题知a=b,且P(2,3)在直线上,代入得: 2/a+3/a=1,因此,a=5,b=5. 所求直线方程为x+y=5. 剖析:直线方程的截距式x/a+y/b=1只适用于ab≠0的形式.
Some classmates are ignorant about the application scope of several types of linear equations when they are seeking linear equations, and some of them are doing improper methods. There are often “leakage” phenomenon. Now we will give a few examples and analyze them. I hope everyone can learn from them. Clarification concept. 1. The use of the intercept formula of the linear equation often leads to leakage solution 1 where P(2,3) is sought and the intercepts on the two axes are equal to each other. Wrong solution: Set the desired linear equation. For x/a+y/b=1. According to the knowledge a=b, and P(2,3) is on the straight line, it is substituted: 2/a+3/a=1, so a=5, b= 5. The required linear equation is x+y=5. Analysis: The intercept formula of the linear equation x/a+y/b=1 only applies to the form of ab≠0.