SOLUTION: y= 3x and y= 3x+10 find the distance between each pair of parallel lines

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Question 357239: y= 3x and y= 3x+10 find the distance between each pair of parallel lines
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Find the perpendicular line that goes through (0,0).
Since perpendicular lines have slopes that are negative reciprocals,
3%2Am2=-1
m2=-1%2F3
y=-%281%2F3%29x%2Bb
Using the origin,
0=-%281%2F3%29%280%29%2Bb
b=0
y=-%281%2F3%29x
Now look for the intersection of y=3x%2B10 and y=-%281%2F3%29x
-%281%2F3%29x=3x%2B10
-x=9x%2B30
-10x=30
x=-3
Then find the y coordinate,
y=%281%2F3%29%283%29=1
Now find the distance from (0,0) to (-3,1) using the distance formula,
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
D%5E2=%28-3-0%29%5E2%2B%281-0%29%5E2
D%5E2=9%2B1
highlight%28D=sqrt%2810%29%29
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