Find the values of k if the lines 2x-5=ky and (k+1)x=6y-3 have the same gradient.

Question

i want the solution of this question in coordinate geometry. please help me as soon as possible 

Answer 1

?????????????? "gradient" ????????? thats the SLOPE

1. 2x-5=ky, y=(2x-5)/k, so slope=2/k

2. (k+1)x=6y-3,   6y=(k+1)x+4,    y=[(k+1)/6]x +2/3...slope=(k+1)/6

same slope...(2/k)=(k+1)/6

(12/k)=k+1

12=k^2+k or k^2+k-12=0

become (k-3)*(k+4) or k=3, -4

Answer 2

Given 2x-5=ky
and (k+1)x=6y-3

Rearrange the equation
ky - 2x + 5 = 0
ky = 2x – 5
y = (2/k)x – 5/k → m1 = 2/k

6y = (k + 1)x - 3
y = (k+1)/6 – 3/6 → m2 = (k + 1)/6

parallel if m1 = m2
2/k = (k + 1)/6
12 = k(k + 1)
12 = k² + k
0 = k² + k – 12
0 = (k + 4)(k – 3)

k = -4 or k = 3

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