Question

Who to find the point-slope form and slope-intercept form of The line passes through the two points (4,-2) and (-8,1)?

Answer 1

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{-8}-\underset{x_1}{4}}} \implies \cfrac{1 +2}{-8 -4} \implies \cfrac{ 3 }{ -12 } \implies - \cfrac{ 1 }{ 4 }`

`\begin{array} \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}{(-2)}=\stackrel{m}{- \cfrac{ 1 }{ 4 }}(x-\stackrel{x_1}{4}) \implies y +2 = - \cfrac{ 1 }{ 4 } ( x -4)`

`y+2=- \cfrac{ 1 }{ 4 }x+1\implies y=- \cfrac{ 1 }{ 4 }x-1 ~~ \impliedby ~~ \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}`