Find the values of k for which the line (k–3) x – (4 – k²) y + k² –7k + 6 = 0 is

Parallel to the x-axis,

The given equation of the

(k–3) x – (4 – k²) y + 6

If the given line is parallel to the x- axis, then

Slope of the given line = Slope of the x- axis.

The given line can be written as

(4 – k²) = (k–3) x + k² –7k + 6 = 0

⇒ y = which is the form y = mx+c

Thus, Slope of the given line =

Slope of x- axis = 0

Then,

⇒ k – 3 = 0

⇒ k = 3

Therefore, if the given line is parallel to the x – axis, then the value of k is 3.