Question

What is an equation of the line that passes through the points (0, -4) and (-4, 6)?

Put your answer in fully reduced form.

Answer 1

`\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{0}}}\implies \cfrac{6+4}{-4}\implies \cfrac{10}{-4}\implies -\cfrac{5}{2}`

`\bf \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}{-\cfrac{5}{2}}(x-\stackrel{x_1}{0}) \\\\\\ y+4=-\cfrac{5}{2}x\implies y=-\cfrac{5}{2}x-4`