Question

find the distance from (-3,1) to 2x-3y=6

Answer 1

It can be less, it can be more..
it can be anything.

Answer 2

y=2/3x-2 use points (-3,1) and( 0,-2)

Answer 3

\[\frac{5}{\sqrt{13}} \approx 4.16025 \]

Answer 4

'distance' means shortest distance

Answer 5

\[distance =\sqrt{(-3-0)^{2}+(1-2)^{2}}\]

Answer 6

sqrt(10)

Answer 7

is this algebra class or calculus?

Answer 8

in any case i can write what i did:
the point where distance will be shortest is on the line perpendicular to
\[2x-3y=6\] through (-3,1)
that line is

\[3x+2y=-7\]

Answer 9

the two lines intersect at
\[(-\frac{9}{13},-\frac{32}{13})\] and the distance between that point and (-3,1) is not what i wrote! it is what saifoo wrote
\[\frac{5}{\sqrt{13}}\]

Answer 10

which is in fact bigger than
\[\sqrt{10}\] so lets see if made a mistake

Answer 11

oh no i see
@ johnny the distance between (-3,1) and (0,-2) is
\[\sqrt{18}=3\sqrt{2}\]

Answer 12

three to the right, three up