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Yomayra · Answer 1 · 2018-05-04T16:26:47+0000

$\bf \stackrel{line~J}{y+8=-(x-2)}\implies y+8=-x+2 \\\\\\ y=-x-6\implies y=\stackrel{slope}{-1}x-6$

now we know the slope of line J is -1.

a line perpendicular to J, will have a negative reciprocal slope, therefore,

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

therefore, line K has a slope of 1, and passes through 3,4,

$\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ % (a,b) &&(~{{ 3}} &,&{{ 4}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies 1 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=1(x-3)\implies y-4=x-3 \\\\\\ y=x+1$

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