Question

What is the equation of the line that passes through (4,3) and (-4,-1)?

Answer 1

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 4 &,& 3~) % (c,d) &&(~ -4 &,& -1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-3}{-4-4}\implies \cfrac{-4}{-8}\implies \cfrac{1}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-3=\cfrac{1}{2}(x-4) \\\\\\ y-3=\cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x+1$