Question

Optimization for calc one.
Find the point on the line -5 x + 6 y - 3 =0 which is closest to the point ( -4, -3 ).

Answer 1

i would solve for \(y\) first then use the distance formula

Answer 2

\[y=\frac{5}{6}x+\frac{1}{2}\]if my algebra is correct

Answer 3

yes, that would be the simplified equation

Answer 4

then a point on the line looks like
\[(x, \frac{5}{6}x+\frac{1}{2})\]

Answer 5

O, I think that was were I was messing up on

Answer 6

the square of the distnance is therefore
\[d^2(x)=(x+4)^2+(x+\frac{1}{2}+3)^2\]

Answer 7

minimize that one

Answer 8

Alright thanks!

Answer 9

yw