A line passes through the points $A,$ $B,$ and $C.$ If $A = (-2,5),$ $B = (-3,1),$ and $C = (4,y),$ then find $y.$
Since the line passes through points $A$ and $B,$ it has slope
\[\frac{1 - 5}{-3 - (-2)} = \frac{-4}{-1} = 4.\]Therefore, the line has equation
\[y - 5 = 4(x + 2).\]Then $y = 4x + 13.$ Substituting the coordinates of $C,$ we find
\[y = 4 \cdot 4 + 13 = \boxed{29}.\]
The slope of the line passing through $A$ and $B$ is
\[\frac{5 - 1}{-2 - (-3)} = \frac{4}{1} = 4.\]Therefore, the equation of this line is
\[y - 5 = 4(x + 2).\]In particular, $y = 5 + 4x.$
The slope of the line passing through $B$ and $C$ is
\[\frac{1 - y}{-3 - 4} = \frac{y - 1}{7} = 4.\]Thus, $4y - 4 = 7,$ so $4y = 11,$ and $y = \boxed{\frac{11}{4}}.$
To find $y,$ we need to consider the equation of the line passing through the points $A,$ $B,$ and $C.$
First, let's find the slope of the line passing through points $A$ and $B.$ The slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula
\[m = \frac{y_2 - y_1}{x_2 - x_1}.\]So the slope of the line passing through points $A$ and $B$ is
\[m_{AB} = \frac{1 - 5}{-3 - (-2)} = -4.\]Next, let's find the equation of the line passing through points $A$ and $B.$ Since the slope is $-4$ and the line passes through the point $A = (-2,5),$ the equation of the line is
\[y - 5 = -4(x + 2).\]Simplifying the right hand side, we find $y - 5 = -4x - 8,$ or $y = -4x - 3.$
We want to find the $y$-coordinate of the point $C$ when $x = 4,$ so we let $x = 4$ in the equation $y = -4x - 3.$ This gives us
\[y = -4(4) - 3 = -19.\]Thus, $y = -19.$ Therefore, the $y$-coordinate of point $C$ is $\boxed{-19}.$