Question 946203
{{{x+7y=6}}}
{{{7y=-x+6}}}
{{{y=-x/7+6/7}}}
{{{m[1]=-1/7}}}
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{{{x-y=4}}}
{{{y=x-4}}}
{{{m[2]=1}}}
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To get the angle between the two lines using the slopes use,
{{{tan(theta)=abs((m[1]-m[2])/(1+m[1]m[2]))}}}
{{{tan(theta)=abs((1-(-1/7))/(1-1/7))=(8/7)/(6/7)=4/3}}}
So then {{{theta=53.13}}}.
The line {{{x-y=4}}} makes a 45 degree angle with the x-axis.
So starting from that slope and rotating clockwise by half of 53.13 will get us to the slope of the bisector.
{{{45-53.13/2=18.43}}}
{{{m=tan(18.43)}}}
{{{m=1/3}}}
Now find the point of intersection of the two lines,
{{{y+4+7y=6}}}
{{{8y=2}}}
{{{y=1/4}}}
Then,
{{{x-1/4=16/4}}}
{{{x=17/4}}}
Now use the point-slope form of a line,
{{{y-1/4=(1/3)(x-17/4)}}}
{{{highlight(y=x/3-7/6)}}}
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{{{drawing(300,300,-2,8,-5,5,grid(1),circle(17/4,1/4,0.25),graph(300,300,-2,8,-5,5,-x/7+6/7,x-4,x/3-7/6))}}}