\[y = kx + b;\ \ \ \ A\ (3;8);\ \ B\ ( - 4;1).\]
\[\left\{ \begin{matrix} 8 = 3k + b\ \ \ \ \ \ (1) \\ 1 = - 4k + b\ \ \ (2) \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[(1) - (2) \Longrightarrow 7 = 7k,\ \ k = 1.\]
\[\left\{ \begin{matrix} k = 1\ \ \ \ \ \ \ \ \ \ \\ b = 8 - 3k \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} k = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ b = 8 - 3 \cdot 1 = 5 \\ \end{matrix} \right.\ \]
\[Уравнение\ прямой:\]
\[y = x + 5.\]