Question

For which value of k so that the lines 2x-3y=9 and kx-12y=18 will be parallel.​

Answer 1

Given that,

$2x-3y=9 ....(1)\\kx-12y=18 ....(2)$

From equation (1) we can find the slope of the line, as

$m_{1} =\frac{2}{3}$

Also from equation(2) we can find slope of the line, as

It is given that the both of the lines are parallel, so their slope of the line will also be equal.

So, we get

$m_{1} =m_{2} \\\frac{2}{3} =\frac{k}{12}$

After cross multiplication we get,

$k*3=2*12\\k=\frac{24}{3} \\k=8$

So, for value of $k=8$ the given lines will be parallel.

Answer 2

Answer:

Consider the given equations.

2x−3y=9

kx−9y=18

Slope of the line

m = 3

1 2

Slope of the line

m =9

2 k

Since, both lines are parallel.

So, the slopes of both lines are equal.

Therefore,

m =m

1 2

3=9

2 k

k=6

Hence, this is the value of k.