急F4 Equations of Straight Line

20.
Slope of L = -2
y-intercept of L = ±4

Then, equation of the L (slope-intercept form) :
y = -2x + 4 or y = -2x - 4


21.(a)
Slope of L :
-k/(-2) = 2
k = 4

21.(b)
L : 4x - 2y + 5 = 0 ...... [1]

Put y = 0 into [1] :
4x + 5 = 0
x = -5/4
x-intercept = -5/4

Put x = 0 into [1]
-2y + 5 = 0
y = 5/2
y-intercept = 5/2


22.
(a)
Put x = 0 and y = 5 into ax + by + 1 = 0
a(0) + b(5) + 1 = 0
5b + 1 = 0
b = -1/5

(b)
Because the two straight lines are //, the slopes of the two straight lines areequal.= :
-a/b = -3/4
a/b = 3/4
a : b = 3 : 4


23.(a)
Slope of L = -1/ [(4 + 2)/(1 + 5)] = -1

Equation of L (slope-intercept form):
y = -x + 1

23.(b)
Put x = 1 and y = 0 into the both sides of the equation :
L.S. = 0
R.S. = -(1) + 1 = 0
Since L.S. = R.S., (1, 0) lies on L.