Given points N (-3; 1) and K (3; -1) find the equation of the straight line NK and the slope.

Because the straight line passes through these points, then the coordinates of the given points satisfy the equation of the straight line of the form y (x) = k * x + b.

To find the desired equation of the line, we solve the system of linear equations:

-3 * k + b = 1 and 3 * k + b = -1.

We add both equations term by term, we get:

2 * b = 0, whence we calculate b = 0.

We now find the slope k from any equation:

3 * k = b – 1 = -1, whence k = -1 / 3.

Therefore, the desired equation of the straight line y (x) = -x / 3.