Question

Write the equation of the line, given the y- and x-intercepts. x-intercept (–6, 0), y-intercept (0, –8)

Answer 1

neverminding for a second that they're intercepts at all, they're points on the line, so

`\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad(\stackrel{x_2}{0}~,~\stackrel{y_2}{-8})\\\\\\ slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-8-0}{0-(-6)}\implies \cfrac{-8-0}{0+6}\implies \cfrac{-8}{6}\implies -\cfrac{4}{3}\\\\\\ \begin{array}c\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-0=-\cfrac{4}{3}[x-(-6)]\\\\\\y=-\cfrac{4}{3}(x+6)\implies y=-\cfrac{4}{3}x-8`