Question

What is the equation of the line that passes through the point left bracket, minus, 3, comma, 4, right bracket(−3,4) and has a slope of minus, 2−2?

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -2 \\\\\\ \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}{-2}(x-\stackrel{x_1}{(-3)}) \implies y -4 = -2 ( x +3) \\\\\\ y -4 = -2 x -6 \implies {\Large \begin{array}{llll} y = -2 x -2 \end{array}}`