Question

4. Use the point-slope formula and the given points to choose the linear equation in slope-intercept form. (8,5),(-4,-1)​

Answer 1

`(\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-1}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{8}}} \implies \cfrac{ -6 }{ -12 } \implies \cfrac{1}{2}`

`\begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{8}) \\\\\\ y-5=\cfrac{1}{2}x-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+1 \end{array}}`