The y - ordinates of $$A_8$$ is

$$x_1 , x_2 , x_3,......., x_n$$ are in A.P. Let the first term be $$a$$ and common difference be $$d$$

Also, $$x_2 = a + d = 2$$

and $$x_{24} = a + 23d = 68$$

Solving above equations, we get : $$a = -1$$ and $$d = 3$$

=> $$x_8 = a + 7d = -1 + 7(3) = 20$$

To find y coordinate, we will use $$y = px + q$$

$$\because A_2 (2, -2)$$ and $$A_{24} (68, 31)$$

Substituting in above equation, => $$-2 = 2p + q$$

and $$31 = 68p + q$$

Solving above equations, we get : $$p = \frac{1}{2}$$ and $$q = -3$$

$$\therefore y_8 = p x_8 + q = \frac{1}{2} (20) + (-3) = 7$$