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How to find distance between two lines... y=3x y=3x+10

Mathematics
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the vertical distance, or horizontal distance or what?
|dw:1350957364620:dw|
that perpendicular line between the two is the distance you want?

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Other answers:

Work out the equation of the perpendicular line. To make t easy, work out the equation of the line that is perpendicular to y=3x and passes through (0,0). Then find the intersection point of this perpendicular line and the other line (y=3x + 10). Then use distance formula.
Hope that makes sense?
yeah, thats what i would do
I am very confused papa. Things are not going well in my house. So can you restart from baby steps? And walk me through the perpendicular lines?
ok, step 1 - do you know the relationship of the slopes of two lines that are perpendicular to one another?
I know that the perpendicular slope is the opposite reciprocal of the slope.
almost - the product of the slopes of two perpendicular lines is always -1.
so - what would be the slope of the line that is perpendicular to y=3x?
-1/3x
perfect - slope would be -1/3, and its equation would be of the form: y = -(1/3)x + c where c is the y-intercept
agreed?
Correct. I got that part.
good, now if we take this perpendicular line such that it passes through the origin, then what would be the value for c?
remember we have: y = -(1/3)x + c and we know y=0 when x=0, therefore c=?
are you stuck?
yes..
C=0
yes - correct
Yay!
so now we know that the line perpendicular to y=3x and that passes through the origin has the equation: y = -(1/3)x
Ok, so i drew that line in on my graph..
|dw:1350958743362:dw|
|dw:1350951532761:dw|
Yea! That!
so next you want to find the point of intersection of: y = -(1/3)x and: y = 3x + 10
Oh ok !
How do i do that...
can you find the point of intersection of these two lines?
just substitue y=-(1/3)x from 1st equation into 2nd equation and solve for x.
then use 1st equation to find the y value once you have the x value
Ah ok!
So like....the answer would be for x=3?
make sure you have the correct sign - does it look like x would be positive here?
aahhhh!!! negative negative!!
:)
now find y value
use the first equation for that, i.e. y = -(1/3)x to find y. remember you just found x=-3
Oh i know i am working it out!!!
y=19
how???
x=-3, therefore:\[y=-\frac{1}{3}\times x=-\frac{1}{3}\times (-3) = ?\]
Oh ok i was using a dif equation.
y=-1
please be more careful in your calculations - try again...
gAAAA
Ohhhhhhhh y=1
good. so now you know the point of intersection is (-3, 1): |dw:1350952783534:dw|
so just use the distance formula to find the distance between (-3,1) and (0,0). That will be the distance between these two lines.
Alright thanks!
yw :)
Now SLEEP! I am ordering my papa to sleep:)

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