MATHS

Slope of L = m

a. Slope of L1 = -(2m + 1)

Since L and L1 are parallel

So the slopes are the same

m = -(2m + 1)

m = -2m – 1

m = -1/3


b. Slope of L2 = -1/(3m + 1)

Since L and L2 are perpendicular

So, slope of L X Slope of L2 = -1

m[-1/(3m + 1)] = -1

m = 3m + 1

m = -1/2

First arrange the equation into the form ---
y = mx+c, where m = slope, c = y-intercept

a/

L1:(2m+1)x+y=0
y= :(2m+1)x

so slope of L1 = 2m+1
and slope of L = m

if L is parallel to the straight line L1, their slope are equal

so, 2m+1 = m
m = -1

b/

L2:x+(3m+1)y-4=0
(3m+1)y = -x +4
y = -x / (3m+1) + 4/(3m+1)

so slope of L2 = -1/(3m+1)
and slope of L = m

If L is perpendicular to the straight line L2, slope of L * slope of L2 = -1

so, (m) * [-1/(3m+1)] = -1
- (m) = -(3m+1)
m = 3m+1
2m = -1
m = -0.5