Question

Write an equation of the line that passes through the points (-2,-2) and (0,5)

Answer 1

`\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -2 &,& -2~) &&(~ 0 &,& 5~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-(-2)}{0-(-2)}\implies \cfrac{5+2}{0+2}\implies \cfrac{7}{2} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-2)=\cfrac{7}{2}[x-(-2)] \\\\\\ y+2=\cfrac{7}{2}(x+2)\implies y+2=\cfrac{7}{2}x+7\implies y=\cfrac{7}{2}x+5`