Question

Find the equation of the line through the points(5/7,0) and (-3,-1). Write your answer in the form y = mx + b

Answer 1

`\bf (\stackrel{x_1}{(5)/(7)}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-0}{-3-(5)/(7)}\implies \cfrac{-1}{~~-(26)/(7)~~} \\\\\\ \cfrac{(-1)/(1)}{~~-(26)/(7)~~}\implies \cfrac{-1}{1}\cdot \cfrac{7}{-26}\implies \cfrac{7}{26}`

`\bf \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-0=\cfrac{7}{26}\left( x-\cfrac{5}{7} \right) \implies y=\cfrac{7}{26}x-\cfrac{5}{26}`