Question 1164905
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that satisfies the given conditions
through (1/2x, - 2/7) perpendicular to the line 4x-8y=1
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Check your document!  The problem should say, "through line with the equation y=(1/2)x-2/7, and perpendicular to line with equation 4x-8y=1.   If that were what the description were intended to mean, it still seems strange.


Perpendicular to  4x-8y=1, would be something of the form  {{{8x+4y=c}}},
{{{4y=-8x+c}}}
{{{highlight(y=-2x+c/2)}}}
and for that, you can let c be any real number.  The line and equation found will be perpendicular to  {{{y=x/2-2/7}}}.