SOLUTION: I've been out sick since Monday and have been getting my work sent home. I've missed this lesson and can't for the life of me figure out how to do this. I've got 10 other similar

Question 570227: I've been out sick since Monday and have been getting my work sent home. I've missed this lesson and can't for the life of me figure out how to do this. I've got 10 other similar problems to do but should be able to figure it out if some kind soul will help me understand.
Calculate the distance from point (-2,3) to the line y=x+1
I would really, really appreciate an explanation not just an answer since I have 9 more of these :)
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Calculate the distance from point (-2,3) to the line y=x+1
-----------
The distance from a point to a line is the shortest distance, which is along the line perpendicular to the given line.
----
The slope, m of y = x + 1 is 1.
The slope of lines perpendicular is the neg inverse, = -1
----
Find the eqn of the line thru the point with a slope of -1.
y = mx + b
3 = -1*(-2) + b
b = 1
----
The line perpendicular thru the point is
y = -x + 1
Find the intersection of the 2 lines.
y = x + 1
y =-x + 1
--------- Add
2y = 2
y = 1
x = 0
The point (0,1) is the intersection.
Find the distance from (0,1) to (-2,3)

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
They want the SHORTest distance from the
point to the line. There are lots of lines you
could draw from the point to the line, but
only 1 is the shortest.
That shortest distance is the perpendicular
from the point to the line.
-----------------------
The 1st thing to do is find the slope of the line.
Get it into the form where
is the slope. ( It's already in that form )
The slope is .
------------------------
Now you want the slope of ANY line which would
be perpendicular to this line.
That formula is ,
so the perpendicular will have slope =
------------------------
Now you have the point (-2,3) and a slope. Use
the point-slope formula to get the equation of
the perpendicular line.

------------------------
Now where do these 2 lines intersect?
Add the equations:

and

So now you have 2 points, (-2,3) and (0,1)
The formula for distance is
distance =
distance =
distance =
distance =
-----------------------
Here's a plot of the line and the line
perpendicular to it going through (-2,3)
The intersection is at (0,1) as you can see

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