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直线与坐标轴所围图形面积的问题,屡屡出现在试题之中,它的特点是数形结合,能较全面地考查学生综合运用知识的能力,现例说如下。一、一条直线与两坐标轴围成直角三角形直角三角形两条直角边落在坐标轴上,它的长分别是直线与x轴、y轴交点纵坐标、横坐标的绝对值。例1 一次函数y=2x+b与两坐标轴围成的三角形面积为4,求b值。(1993年黑龙江中考题) 解如图1,直线y=2x+b与x轴、y
The problem of graphic area enclosed by lines and axes often appears in the questions. It is characterized by a combination of numbers and shapes, and can comprehensively examine the students’ ability to use knowledge comprehensively. The current example is as follows. First, a straight line and two coordinate axes form a right-angled triangle. Two right-angled triangles fall on the coordinate axis, and their lengths are the absolute values of the straight line, the ordinate and the y-axis at the intersection point, and the abscissa. Example 1 The quadratic function y = 2x + b and the area of the triangle surrounded by the two coordinate axes is 4, find the value of b. (1993 Heilongjiang examination questions) Solution Figure 1, straight line y=2x+b and x axis, y