Question

Write an equation of a line in Slope Intercept from that passes through the points (3, -2) and 1,4

Answer 1

`\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-2)}{1-3}\implies \cfrac{4+2}{1-3}\implies \cfrac{6}{-2}\implies -3 \\\\\\ \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-(-2)=-3(x-3) \\\\\\ y+2=-3x+9\implies y=-3x+7`