Question

What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −2/3?

y+7=2/3(x+1)

y−7=−2/3(x+1)

y−7=2/3(x−1)

y+7=−2/3(x−1)

Answer 1

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{2}{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}{(-7)}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{1}) \implies y +7 = -\cfrac{2}{3} ( x -1)`