For what values of k are the lines kx + 3y + 5 = 0 and (k + 1) x-2y-1 = 0 parallel?

Let us bring the equations of the straight lines to the form y = c * x + b.

kx + 3y + 5 = 0;

3y = -kx – 5;

y = -k / 3 * x – 5/3.

(k + 1) x – 2y – 1 = 0;

-2y = – (k + 1) * x + 1;

y = 2 (k + 1) * – 1/2.

The condition for the parallelism of straight lines is the equality of the coefficients at x, we obtain the equation for k:

-k / 3 = 2 (k + 1);

-k = 6k + 6;

5k = -6;

k = -6/5.

Answer: the required value of the parameter k was -6/5.