Finding the Value of y in Coordinate Geometry

In the coordinate plane, points A(2, 3), B(6, 7), and C(x, y) form a triangle. The area of triangle ABC is given by the formula:

$$ ext{Area} =\frac{1}{2} | x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) | $$

where $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ are the coordinates of points A, B, and C respectively. If the area of triangle ABC is 14, what is the possible value of $y$ when $x = 4$?