The pair of points (6, y) and (10, -1) lie on a line with slope 1/4. What is the value of y?
We use the formula for the slope between two points $(x_1,y_1)$ and $(x_2,y_2),$ \begin{align*}
\text{slope}&=\frac{y_2-y_1}{x_2-x_1}. \\
\Rightarrow\qquad \frac{1}{4}&=\frac{-1-y}{10-6}=\frac{-1-y}{4}.
\end{align*}Multiplying by 4 and solving \[
-1-y=4\cdot \frac{1}{4}=1\qquad\Rightarrow\qquad y=\boxed{-2}.
\]