Question

Find the equation of a line that passes through the points (-1,5) and (3,-3). Write the equation in slope-intercept, point-slope, and standard form.

Answer 1

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-5}{3-(-1)}\implies \cfrac{-3-5}{3+1}\implies -2 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=-2[x-(-1)] \\\\\\ \boxed{y-5=-2(x+1)}\implies y-5=-2x-2\implies \boxed{\stackrel{slope-intercept~form}{y=-2x+3}} \\\\\\ \boxed{\stackrel{standard~form}{2x+y=3}}$