Question

What is the x intercept of the equation that passes through (1,-6) and is perpendicular to y=1/3x +1

Answer 1

$\bf y=\stackrel{slope}{\cfrac{1}{3}}x+1\impliedby \textit{slope of this line, so a perpendicular will be} \\\\\\ \textit{perpendicular, negative-reciprocal slope for}\quad \cfrac{1}{3}\\\\ negative\implies -\cfrac{1}{ 3}\qquad reciprocal\implies - \cfrac{ 3}{1}\implies -3\\\\ -------------------------------\\\\ \begin{array}{ccccccccc} &&x_1&&y_1\\ &&(~1 &,& -6~) \end{array}$

$\bf slope = m\implies -3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-6)=-3(x-1) \\\\\\ y+6=-3x+3\implies 0+6=-3x+3\implies 3=-3x\implies \cfrac{3}{-3}=x \\\\\\ -1=x\qquad \qquad \qquad \qquad \qquad \qquad \qquad (~-1~,~0~)$