Question

Find the equation of a line that passes through the point (5,3) and has a gradient of -2. Leave your answer in the form y=mx+c​

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}c \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}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{5}) \\\\\\ y-3=-2x+10\implies {\Large \begin{array}{llll} y=-2x+13 \end{array}}`