Question

Find the point on the line y = 6x closest to the point (1, 0).

Answer 1

I'm guessing it would be on a line containing the point (1,0) with slope perpendicular to y = 6x.

Answer 2

yeap

Answer 3

make a graph, plot three points, draw a line and your answer will jump out at you.

Answer 4

what would be the equation of a line perpendicular to y = 6x that passes through ( 1, 0 ) ?

once you get that equation, you'd have 2 equations, one for each line

solve the system of equations, that is, where they meet, AT THAT POINT, is the closest point to ( 1, 0 )

since it's perpendicular to it and thus the most direct path to it

Answer 5

slope of perpendicular line = m1*m2=-1
6*m2=-1
m2=-1/6
find equation of line passing through (1,0) and with slope (-1/6)
and find intersection point of this line with y=6x
that will be your required point