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Spencer R · Answer 1 · 2018-10-28T12:19:01+0000

let's take a peek at 7x + 4 for a second,
$\bf y = \stackrel{slope}{7}x\stackrel{y-intercept}{+4}$

well well, it has a slope of 7.

now, a line perpendicular to that one, will have a negative reciprocal slope,

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad 7\implies \cfrac{7}{1}\\\\ negative\implies -\cfrac{7}{{{ 1}}}\qquad reciprocal\implies - \cfrac{{{ 1}}}{7}$

so, we're really looking for the equation of a line whose slope is -1/7 and runs through -4, -2

$\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ % (a,b) &&(~{{ -4}} &,&{{ -2}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies -\cfrac{1}{7} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-2)=-\cfrac{1}{7}[x-(-4)] \\\\\\ y+2=-\cfrac{1}{7}(x+4)\implies y+2=-\cfrac{1}{7}x-\cfrac{4}{7} \\\\\\ y=-\cfrac{1}{7}x-\cfrac{4}{7}-2\implies y=-\cfrac{1}{7}x-\cfrac{18}{7}$

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