F.5直線方程......

(a) L1的斜率 = -4
L⊥L1
L的斜率 x L1的斜率 = -1
L的斜率 = -1/(-4)
L的斜率 = 1/4

(b) L的方程:
y - 3 = 1/4(x-5)
y = x/4 + 7/4

(c) L1 : 4x+y-6 = 0 ---(1)
L : y = x/4 + 7/4 ---(2)
考慮(1), y = 6 - 4x ---(3)
代入(3)於(2),
6-4x = x/4 + 7/4
24-16x = x+7
17x = 17
x = 1
代入x = 1 於(3),
y = 6-4(1) = 2
L和L1的交點是(1,2)

a)
L的斜率 x L1的斜率 = -1

L1的斜率 : y = -4x + 6 , -4

L的斜率 = -1/-4 = 1/4

b)
y = mx + c

3 = 5/4 + c

c = 7/4

L:y = x/4 + 7/4

L:x - 4y + 7 = 0

c)
4x + y - 6 = 0 ... (1)

x - 4y + 7 = 0 ... (2)

(2), 4x - 16y + 28 = 0

(1) - (2),

17y - 34 = 0

y = 2

So, 4x - 16y + 28 = 0

x = (-28 + 16*2) = 4/4 = 1

So, 交點坐標(1,2)