中四數學~急...

將兩絛line寫為 : y = mx + c , where m 是個slope 斜率

L1:(k+2)x+(2k-1)y-10=0
y = ( -(k+2)x + 10 ) / (2k-1)
y = -( (k+ 2)/(2k-1) ) * x + 10 /(2k-1)

so m of L1 = -( (k+ 2)/(2k-1) )

L2 : x/2-y/3=1
x/2 -1 = y/3
3x/2 -3= y
y = 3x/2 -3

so m of L2 = 3/2

if L1 and L2 互相平行
m of L1 = m of L2
-(k+2)/(2k-1) = 3/2
-2k - 4 = 6k -3
8k = -1
k = -1/8

(k+2)x+(2k-1)y=10 // 1/2x-1/3y=1
(k+2)x+(2k-1)y=10 // 5x-10/3y=10

(k+2)/(2k-1) = 5/(-10/3)
(k+2)(-10/3) = 5(2k-1)
.....
識做la之後^^