ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 836

\[\boxed{\text{836.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[y = kx + b - график\ линейной\ \]

\[функции.\]

\[\textbf{а)}\ ( - 1;3)\ и\ (2; - 2)\]

\[\left\{ \begin{matrix} - k + b = 3\ \ \\ 2k + b = - 2 \\ \end{matrix} \right.\ ( - )\]

\[- 3k = 5\]

\[k = - \frac{5}{3} = - 2\frac{1}{3};\]

\[b = 3 + k = 3 - 2\frac{1}{3} = \frac{2}{3}.\]

\[Линейная\ функция\ имеет\ вид:\]

\[y = - 2\frac{1}{3}x + \frac{2}{3}.\]

\[\textbf{б)}\ (4;1)\ и\ ( - 3; - 1)\]

\[\left\{ \begin{matrix} 4k + b = 1\ \ \ \ \ \ \ \\ - 3k + b = - 1 \\ \end{matrix} \right.\ ( - )\]

\[7k = 2\]

\[k = \frac{2}{7}.\]

\[b = 1 - 4k = 1 - 4 \cdot \frac{2}{7} =\]

\[= 1 - \frac{8}{7} = - \frac{1}{7}.\]

\[Линейная\ функция\ имеет\ вид:\]

\[y = \frac{2}{7}x - \frac{1}{7}.\]

\[\textbf{в)}\ (0;5)\ и\ (4;0)\]

\[\left\{ \begin{matrix} 0k + b = 5 \\ 4k + b = 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} b = 5\ \ \ \ \ \ \\ 4k = - b \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} b = 5\ \ \ \ \\ k = - \frac{5}{4} \\ \end{matrix} \right.\ \]

\[Линейная\ функция\ имеет\ вид:\]

\[y = - 1\frac{1}{4}x + 5.\]

\[\textbf{г)}\ ( - 3;0)\ и\ (0; - 6)\]

\[\left\{ \begin{matrix} - 3k + b = 0 \\ 0k + b = - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} b = - 6 \\ 3k = b \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\ \left\{ \begin{matrix} b = - 6 \\ k = - 2 \\ \end{matrix} \right.\ \]

\[Линейная\ функция\ имеет\ вид:\]

\[y = - 2x - 6.\]