\[y = kx + b;\ \ \ A(2;1);\ \ B( - 4;10).\]
\[Подставим\ координаты\ точек\ в\ \]
\[уравнение\ прямой\ и\ запишем\]
\[систему:\]
\[\left\{ \begin{matrix} 2k + b = 1\ \ \ \ \ \\ - 4k + b = 10 \\ \end{matrix} \right.\ ( - )\]
\[6k = - 9\]
\[k = - 1,5.\]
\[\left\{ \begin{matrix} b = 1 - 2k \\ k = - 1,5\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} b = 1 + 3 \\ k = - 1,5\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} b = 4\ \ \ \ \ \ \ \\ k = - 1,5 \\ \end{matrix} \right.\ \]
\[Уравнение\ прямой:\]
\[y = - 1,5x + 4.\]