SOLUTION: Hello! I'm having trouble breaking down problems like the following: Find the distance from (-6,2) to the line defined by y=-2x-5. Express as a radical or a number rounded to

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Question 984199: Hello! I'm having trouble breaking down problems like the following:
Find the distance from (-6,2) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth.
If you could please explain the steps to solve this problem as simple as possible it would be greatly appreciated!
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
The given line y=-2x-5 can be represented as an ordered pair (x, -2x-5), since y is equated to the expression -2x-5. What you really want is the point of intersection for y=-2x-5 and the line from (-6,2) perpendicular to y=-2x-5. Then you want the distance between these two points.

Line with m=1%2F2 containing point (-6,2)?
Perpendicular lines in a plane have slopes which are negative reciprocal of each other.
y-2=%281%2F2%29%28x-%28-6%29%29, using point slope form.
y=%281%2F2%29x%2B2%2A6%2B2
y=x%2F2%2B14

Intersection of y=x%2F2%2B14 and y=-2x-5 ?
x%2F2%2B14=-2x-5
x%2B28=-4x-10
5x=-28-10
x=-38%2F5
-
y=51%2F5

Distance Formula for distance between (-38/5,51/5) and (-6,2) ?
highlight_green%28sqrt%28%28-6-%28-38%2F5%29%29%5E2%2B%282-51%2F5%29%5E2%29%29
some simplification and computation still needed.