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高三数学教学中,师生经常遇到类似例题:例1已知点A(1,4),B(3,1),直线l:y=ax+2与线段AB相交于点P,求l的斜率的取值范围[1].为解决这类问题,教师会给学生设计台阶,以“利”学生能够按照教师预设的方向,做出该题:例2已知点A(-2,4),B(1,3),直线l:y=ax+2与线段AB相交于点P,(1)求直线l的倾斜角α的取值范围;(2)求直线l的斜率的取值范围.这一设计的好处在于能够直观地看到直线l的倾斜角的变化,然后,再利用正切函数的性质,求出直线
Senior high school mathematics teaching, teachers and students often encounter similar examples: Example 1 Known point A (1,4), B (3,1), the line l: y = ax + 2 and the line AB intersects at point P, The slope of the range [1] .To solve such problems, teachers will give students design steps to “Lee” students can follow the direction of the teacher to make the question: Example 2 Known point A ( (4), B (1,3), the line l: y = ax + 2 intersects the line segment AB at the point P, (1) Find the range of inclination angle α of the line l; (2) Find the line l Of the slope of the value of this design has the advantage of being able to visually see the straight line l tilt angle changes, and then use the nature of the tangent function, find the straight line