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Make a perpendicular to the line that has an x-intercept of 8, or (8,0). It has a slope of 3 (negative reciprocal). The equation of that line is y=3x-24, using the point slope formula of y-y1=m(x-x1)=3(x-8)
Find where it intersects the other line with equation y=(-x/3)+(2/3).
Now write both in standard form and solve
-3x+y=-24
x+3y=2
3x+9y=6, multiplying by 3
10y=-18
y=-1.8
substitute into the second equation and x-5.4=2
x=7.4
Check in the first: -22.2-1.8=-24
So, we want the distance between (7.4,-1.8) and (8,0)
sqrt(1.8^2+0.36)=sqrt(3.6)=1.897 or 1.9 units
