Question

Find the slope-intercept equation of the line that passes through
(4,4) and has a slope of 1/3

Answer 1

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}ll \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}{4}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{4}) \\\\\\ y-4=\cfrac{1}{3}x-\cfrac{4}{3}\implies y=\cfrac{1}{3}x-\cfrac{4}{3}+4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{8}{3} \end{array}}`