To find the set of values of k for which the line does not intersect the curve, we substitute y from the line equation into the curve equation:

\(y = \frac{x + k}{2}\)

Substitute into the curve equation:

\(\frac{x + k}{2} = x^2 - 4x + 7\)

Multiply through by 2 to eliminate the fraction:

\(x + k = 2x^2 - 8x + 14\)

Rearrange to form a quadratic equation:

\(2x^2 - 9x + 14 - k = 0\)

For the line not to intersect the curve, the discriminant of this quadratic must be less than zero:

\(b^2 - 4ac < 0\)

Here, a = 2, b = -9, c = 14 - k. Calculate the discriminant:

\((-9)^2 - 4 \times 2 \times (14 - k) < 0\)

\(81 - 8(14 - k) < 0\)

Simplify:

\(81 - 112 + 8k < 0\)

\(8k < 31\)

\(k < \frac{31}{8}\)

Thus, the set of values of k for which the line does not intersect the curve is:

\(k < 3.875\)