Question

Which choices are equations for the coordinates (-2,4) (1,-2)?

Answer 1

$\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-4}{1-(-2)}\implies \cfrac{-2-4}{1+2}\implies \cfrac{-6}{3}\implies -2 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=-2[x-(-2)]\implies y-4=-2(x+2)$