Question

Write the equation of the line that passes through the given points.
(2,0.5) and (0,3.5)

Answer 1

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{0.5})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3.5}-\stackrel{y1}{0.5}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{2}}} \implies \cfrac{3}{-2}\implies -\cfrac{3}{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}{0.5}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{2}) \\\\\\ y-0.5=- \cfrac{3}{2}x+3\implies y==- \cfrac{3}{2}x+3+0.5\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x+3.5 \end{array}}`