Question

直线y=x-2与y轴交与点A,直线y=kx+b与y轴交与B,且与y=x-2交与点C,已知点C的纵坐标为1，且S△ABC=9，求k与b

Answer 1

x = 0, y = 0 - 2 = -2, A(0, -2)
C的纵坐标为1: 1 = x - 2, x = 3, C(3, 1)

设B(0,b)
S△ABC=9 = (1/2)|AB|*C的横坐标
= (1/2)|b + 2|*3 = (3/2)|b + 2|
|b + 2| = 6
(i)

b + 2 = 6, b = 4, B(0, 4)
直线y=kx+b, x = 0, y = b = 4
过C(3, 1): 1 = 3k + 4, k = -1

或

(ii)

b+2 = -6, b = -8, B(0, -8)
直线y=kx+b, x = 0, y = b = -4
过C(3, 1): 1 = 3k - 8, k = 3