Question

直线的倾斜角与斜率 例1、例2

Answer 1

|k| < 1,-1 < k = tanα < 1

0 ≤ k < 1:0 ≤ α < π/4

-1 < k < 0:3π/4 < α < π

系数成比例(但不与常数项成比例)时, 二者平行:

1 :2m = 1 + m :4

m² + m - 2 = (m + 2)(m - 1) = 0

m = -2: 此时二直线均可变为x - y = 4, 舍去m = -2

m = 1: 此时二直线平行

二者可分别变为y = -x/(1 + m) + (2 - m)/(1 + m)和y = -mx/2 - 4,斜率分别为-1/(1 + m),-m/2

其积为[-1/(1 + m)](-m/2) = -1

m = -2/3

m≠ -2且m ≠ 1时,二者相交