math equation

a)
because Kx+4y=1, 3x+y=2+kx
so yL1=(-kx/4)-(1/4), and yL2=x(k-3)+2
because they are parrele to each other, the slope of the two equations are equal
so that, we can get
(-k/4)=k-3
so 5k=12, k=12/5

b)
because k=12/5, we can get L2=3x+y=2+12/5x, so y=(-3/5)x+2
for x-intercept, y=0, so 0=(-3/5)x+2, x=10/3
so that, the x-intercept of L3 will be 4+10/3=22/3 with the same slope with L2
so, we can know the information below:
point=(22/3,0), slope=-3/5
use the equationy-y0=m(x-x0)
y=(-3/5)(x-22/3)
i hope it's helpful

L1: Kx+4y=1
y=-K/4 x + 1/4
Therefore the gradient of L1 is -K/4.
L2: 3x+y=2+Kx
y=(K-3)x+2
Therefore the gradient of L2 is (K-3).
Because L1 and L2 are parallel.
Therefore the gradients are equal.
-K/4=K-3
K=-4K+12
5K=12
K=12/5

(b)
L2: y=(K-3)x+2
y=-3/5 x+2
x=-5/3 y- 10/3
The x-intercept of L2 is -10/3.
Because L2 and L3 are parallel.
Therefore their gradients are equal.
Because the x-intercept of L3 is greater than L2 s by 4.
Therefore the x-intercept of L3 is -10/3+4=2/3
Therefore the equation of L3:x=-3/5 y+ 2/3
L3: y=-5/3 x - 10/9