Question

Write a detailed equation in slope-intercept form for the line that passes through (3,1) and (1,2).

25 points

Answer 1

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ 1 }{ -2 } \implies - \cfrac{1 }{ 2 }`

`\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}{1}=\stackrel{m}{- \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{3}) \\\\\\ y-1=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}\implies y=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}+1\implies {\Large \begin{array}{llll} y=- \cfrac{1 }{ 2 }x+\cfrac{5}{2} \end{array}}`