我想問關於直線幾何的math

若A(3,4)、B(-2,-3) C(k,-2)三點共線, 則
AB的斜率 = BC的斜率
[4 - (-3)] / [3 - (-2)] = [-3 - (-2)] / [-2 - k]
7 / 5 = -1 / (-2 - k)
7(-2 - k) = -5
-2 - k = -5 / 7
k = -2 + 5 / 7
k = -9 / 7