karatechopper
  • karatechopper
How to find distance between two lines... y=3x y=3x+10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
the vertical distance, or horizontal distance or what?
karatechopper
  • karatechopper
|dw:1350957364620:dw|
anonymous
  • anonymous
that perpendicular line between the two is the distance you want?

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asnaseer
  • asnaseer
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.
asnaseer
  • asnaseer
Hope that makes sense?
anonymous
  • anonymous
yeah, thats what i would do
karatechopper
  • karatechopper
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?
asnaseer
  • asnaseer
ok, step 1 - do you know the relationship of the slopes of two lines that are perpendicular to one another?
karatechopper
  • karatechopper
I know that the perpendicular slope is the opposite reciprocal of the slope.
asnaseer
  • asnaseer
almost - the product of the slopes of two perpendicular lines is always -1.
asnaseer
  • asnaseer
so - what would be the slope of the line that is perpendicular to y=3x?
karatechopper
  • karatechopper
-1/3x
asnaseer
  • asnaseer
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
asnaseer
  • asnaseer
agreed?
karatechopper
  • karatechopper
Correct. I got that part.
asnaseer
  • asnaseer
good, now if we take this perpendicular line such that it passes through the origin, then what would be the value for c?
asnaseer
  • asnaseer
remember we have: y = -(1/3)x + c and we know y=0 when x=0, therefore c=?
asnaseer
  • asnaseer
are you stuck?
karatechopper
  • karatechopper
yes..
karatechopper
  • karatechopper
C=0
asnaseer
  • asnaseer
yes - correct
karatechopper
  • karatechopper
Yay!
asnaseer
  • asnaseer
so now we know that the line perpendicular to y=3x and that passes through the origin has the equation: y = -(1/3)x
karatechopper
  • karatechopper
Ok, so i drew that line in on my graph..
karatechopper
  • karatechopper
|dw:1350958743362:dw|
asnaseer
  • asnaseer
|dw:1350951532761:dw|
karatechopper
  • karatechopper
Yea! That!
asnaseer
  • asnaseer
so next you want to find the point of intersection of: y = -(1/3)x and: y = 3x + 10
karatechopper
  • karatechopper
Oh ok !
karatechopper
  • karatechopper
How do i do that...
asnaseer
  • asnaseer
can you find the point of intersection of these two lines?
asnaseer
  • asnaseer
just substitue y=-(1/3)x from 1st equation into 2nd equation and solve for x.
asnaseer
  • asnaseer
then use 1st equation to find the y value once you have the x value
karatechopper
  • karatechopper
Ah ok!
karatechopper
  • karatechopper
So like....the answer would be for x=3?
asnaseer
  • asnaseer
make sure you have the correct sign - does it look like x would be positive here?
karatechopper
  • karatechopper
aahhhh!!! negative negative!!
asnaseer
  • asnaseer
:)
asnaseer
  • asnaseer
now find y value
asnaseer
  • asnaseer
use the first equation for that, i.e. y = -(1/3)x to find y. remember you just found x=-3
karatechopper
  • karatechopper
Oh i know i am working it out!!!
karatechopper
  • karatechopper
y=19
asnaseer
  • asnaseer
how???
asnaseer
  • asnaseer
x=-3, therefore:\[y=-\frac{1}{3}\times x=-\frac{1}{3}\times (-3) = ?\]
karatechopper
  • karatechopper
Oh ok i was using a dif equation.
karatechopper
  • karatechopper
y=-1
asnaseer
  • asnaseer
please be more careful in your calculations - try again...
karatechopper
  • karatechopper
gAAAA
karatechopper
  • karatechopper
Ohhhhhhhh y=1
asnaseer
  • asnaseer
good. so now you know the point of intersection is (-3, 1): |dw:1350952783534:dw|
asnaseer
  • asnaseer
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.
karatechopper
  • karatechopper
Alright thanks!
asnaseer
  • asnaseer
yw :)
karatechopper
  • karatechopper
Now SLEEP! I am ordering my papa to sleep:)

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