Question

What is the equation of the line that has a slope of -1/3 and passes through the point (-4,1/3)

Answer 1

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{(1)/(3)})\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}{\cfrac{1}{3}}=\stackrel{m}{-\cfrac{1}{3}}(x-\stackrel{x_1}{(-4)}) \implies y-\cfrac{1}{3}=-\cfrac{1}{3}(x+4)`

`y-\cfrac{1}{3}=-\cfrac{1}{3}x-\cfrac{4}{3}\implies y=-\cfrac{1}{3}x-\cfrac{4}{3}+\cfrac{1}{3}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x-1 \end{array}}`