Question 345409
Find the intersection point.
{{{ 7x-4y=8}}}
{{{7(24)-4y=8}}}
{{{168-4y=8}}}
{{{-4y=-160}}}
{{{y=40}}}
({{{24}}},{{{40}}})
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Now find the perpendicular line,
{{{7x-4y=8}}}
{{{-4y=-7x+8}}}
{{{y=(7/4)x-2}}}
Perpendicular lines have slopes that are negative reciprocals,
{{{m1*m2=-1}}}
{{{(7/4)*m2=-1}}}
{{{m2=-4/7}}}
Use the point-slope form of a line, {{{y=mx+b}}}
{{{y=-(4/7)x+b}}}
USe the point ({{{24}}},{{{40}}}) to solve for {{{b}}}.
{{{40=-(4/7)(24)+b}}}
{{{b=280/7+96/7}}}
{{{b=376/7}}}
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{{{highlight(y=-(4/7)x+376/7)}}}
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{{{drawing(300,300,-10,50,-10,50,grid(1),circle(24,40,0.9),graph(300,300,-10,50,-10,50,(7/4)x-2,-(4/7)x+376/7))}}}