Find the value of k such that the following two lines are parallel.

Question

Find the value of k such that the following two lines are parallel.

2​x​ + ​y​ =5 ; ​x​ – k​y​ = 7

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4