Given two straight lines x 3y 2 and 3x ky 4 0 if the two lines are parallel the value of k is

First, put each equation into slope-intercept form. This will help because we will then have a slope for each equation. As a reminder the slope-intercept form looks like:

The coefficient 'm' is the slope of the line

The first one looks like...

subtract the 1 and the 3x from each side to get

The slope of this line is -3/4. The next equation looks like...

ky = -4x - 3 after doing similar operations.

We don't care about the -3/k term at the far right because that is the intercept. We only care about the slope term, because the problem wants us to find k such that the the lines are parallel. The thing that makes any two lines parallel is that their slopes have the same value. Thus, we want (-4/k) to be equal to (-3/4).

First, those pesky negatives cancel out.

Now you can cross-multiply to get

Now divide by 3 so that you isolate 'k'

Hey! We have now found 'k' such that the two lines are parallel.

I hope this helps! Please let me know if you have any questions.

Put 2​x​ + ​y​ =5 into the slope intercept form y = 5 - 2x. The slope is -2. If the lines are parallel, the slopes must be equal. Put the equation x​ – k​y​ = 7 into the slope intercept form y = x/k -7/k.

For the slopes to be equal, 1/k = -2 or k = -1/2, so the equation becomes y = -2x +14

Rewrite both equations in y = mx+b form

y = -2x +5

ky = x-7 --> y = (x -7)/k --> y = x/k - 7/k

To make the lines parallel, both lines need to have the same slope which is -2.

1/k = -2 --> k = -1/2

The slopes of both lines must be equal in order to be parallel.

First line can be y = -2x + 5, so slope is -2

Second line can be y = (1/k)x - 7/k, so slope is 1/k

Since slopes must be equal, then -2 = 1/k , or -2k = 1, or k = -1/2