to find the point, find the location
realize that the shortest line that crosses through the origin and y=9x+8 is perpendicular to y=9x+8
perpendicular lines have slopes that multiply to get -1
y=9x+8 has a slope of 9
9*m=-1, m=-1/9
the slope of the mystery line is -1/9
since it passes through the origin, the y intercept is 0
y=(-1/9)x is the equation of the line from the point to the origin
find the intersection of this line and the original line
set them equal to each other
(-1/9)x=9x+8
multily both sides by 9
-x=81x+72
minus 81 both sides
-82x=72
divide both sides by -82
x=-36/41
find y
y=(-1/9)x
y=(-1/9)(-36/41)
y=4/41
the point is [tex](\frac{-36}{41},\frac{4}{41})[/tex]
