A line passes through the points $A,$ $B,$ and $C.$ If $A = (-2,5),$ $B = (-3,1),$ and $C = (4,y),$ then find $y.$
We proceed as follows. Since a line passes through $(x_1, y_1)$ and $(x_2, y_2),$ we know that the slope of the line is
\[\frac{y_2 - y_1}{x_2 - x_1}.\]Hence, the slope of the line passing through $A$ and $B$ is
\[\frac{1 - 5}{-3 - (-2)} = 1,\]so the line is of the form $y - 5 = 1 (x + 2).$ Also, $C = (4,y)$ must lie on this line, so substituting in, we get
\[y - 5 = x + 2.\]Therefore, $y = x + 7.$
Thus, the $y$-coordinate of $C$ is $\boxed{11}.$
To find the value of $y,$ we need to determine the coordinates of point $C.$
We can use the equation of a line passing through two points to find the equation of the line passing through $A = (-2,5)$ and $B = (-3,1).$ The equation of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ can be expressed as
$$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1).$$
Substituting $A = (-2,5)$ and $B = (-3,1),$ we have
$$y - 5 = \frac{1 - 5}{-3 - (-2)}(x - (-2)).$$
Simplifying, we have
$$y - 5 = -4(x + 2).$$
Expanding and simplifying, we find
$$y - 5 = -4x - 8.$$
To find the equation of the line passing through points $A,$ $B,$ and $C,$ we can use the slope-intercept form of the equation of a line, which is $y = mx + b,$ where $m$ is the slope and $b$ is the $y$-intercept.
We can start by finding the slope of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1},$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of two points on the line.
Let's find the slope using points $A = (-2,5)$ and $B = (-3,1):$
\[m = \frac{1 - 5}{-3 - (-2)} = \frac{-4}{-1} = 4.\]
Now that we have the slope, we can use it to form the equation of the line passing through point $A.$
Let's substitute the coordinates of point $A$ into the slope-intercept form, and solve for $b:$
\[5 = 4 \cdot (-2) + b.\]
Simplifying, we have $-8 + b = 5,$ which gives us $b = 13.$
Therefore, the equation of the line passing through points $A$ and $B$ is $y = 4x + 13.$
To find the value of $y$ for point $C = (4,y),$ we can substitute $x = 4$ into the equation of the line:
\[y = 4(4) + 13 = 16 + 13 = 29.\]
Hence, $y = \boxed{29}.$