Slope Equality in Coordinate Geometry

Consider the points A(2, 3), B(6, 7), and C(k, 11) in the Cartesian plane. The point C is such that the slope of line segment AB is equal to the slope of line segment AC. Find the value of k.

Recall that the slope of a line segment between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$