Question 932360
Why just find x instead of further finding reciprocal?  


You want to know the equation for the line perpendicular and containing point (-7,1), and then find the intersection of this with the given line, with most interest on the x value.


GIVEN  {{{y=x+4}}}, FIND equation of line of slope -1 which contains (-7,1).  This line is {{{y-1=-1(x-(-7))}}} according to point-slope form.
{{{y=1-(x+7)}}}
{{{y=1-x-7}}}
{{{y=-x-6}}}
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Equate the two expressions for y, between the two different lines.
{{{x+4=-x-6}}}
{{{2x=-10}}}
{{{highlight(x=5)}}}
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Reciprocal wanted is {{{highlight(1/x=1/5)}}}.