Question

what equation in slope-intercept form represents the line that passes through the points (-3,4) and (2,-1)

Answer 1

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -3 &,& 4~) % (c,d) &&(~ 2 &,& -1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{2-(-3)}\implies \cfrac{-1-4}{2+3}\implies -\cfrac{5}{6}$

$\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=-\cfrac{5}{6}[x-(-3)] \\\\\\ y-4=-\cfrac{5}{6}(x+3)\implies y-4=-\cfrac{5}{6}x-\cfrac{5}{2} \\\\\\ y=-\cfrac{5}{6}x-\cfrac{5}{2}+4\implies y=-\cfrac{5}{6}x+\cfrac{3}{2}$