Question

What’s the equation for the order pairs (1,-5) and (-2,5)

Answer 1

$\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-(-5)}{-2-1}\implies \cfrac{5+5}{-2-1}\implies \cfrac{10}{-3}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=-\cfrac{10}{3}(x-1)\implies y+5=-\cfrac{10}{3}x+\cfrac{10}{3} \\\\\\ y=-\cfrac{10}{3}x+\cfrac{10}{3}-5\implies y=-\cfrac{10}{3}x-\cfrac{5}{3}$