Plz help me in solving these questions of coordiante geomatery?

Question

The straight lines kx = 4y + 5 and (2k + 2)x = 7- 6y are parallel. Find k.

Answer 1

Write both as y=mx+n where m is the slope
y=k/4 x -5/4

y= -(k+1)/3 x +7/6 Both slopes must be equal so

k/4=-(k+1)/3====> 3k = -4k-4 7k=-4 k= - 4/7

Answer 2

if they rparallel=slopes r equal
kx=4y+5
kx-5=4y slope=k/4

//ly(2k+2)x=7-6y
2kx+2x-7=-6y
slope=2k+2/-6 -3k=4k+4 *k=-4/7

Answer 3

m1=k/4 and m2=(2k+2)/(-6)

we know m1=m2 thus k/4=(2k+2)/(-6) => -6k=8k+8 then

-14k=8 => k=8/(-14)=-4/7