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

- karatechopper

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

- Stacey Warren - Expert brainly.com

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- schrodinger

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- anonymous

the vertical distance, or horizontal distance or what?

- karatechopper

|dw:1350957364620:dw|

- anonymous

that perpendicular line between the two is the distance you want?

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## More answers

- 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

Hope that makes sense?

- anonymous

yeah, thats what i would do

- 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

ok, step 1 - do you know the relationship of the slopes of two lines that are perpendicular to one another?

- karatechopper

I know that the perpendicular slope is the opposite reciprocal of the slope.

- asnaseer

almost - the product of the slopes of two perpendicular lines is always -1.

- asnaseer

so - what would be the slope of the line that is perpendicular to y=3x?

- karatechopper

-1/3x

- 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

agreed?

- karatechopper

Correct. I got that part.

- 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

remember we have:
y = -(1/3)x + c
and we know y=0 when x=0, therefore c=?

- asnaseer

are you stuck?

- karatechopper

yes..

- karatechopper

C=0

- asnaseer

yes - correct

- karatechopper

Yay!

- 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

Ok, so i drew that line in on my graph..

- karatechopper

|dw:1350958743362:dw|

- asnaseer

|dw:1350951532761:dw|

- karatechopper

Yea! That!

- asnaseer

so next you want to find the point of intersection of:
y = -(1/3)x
and:
y = 3x + 10

- karatechopper

Oh ok !

- karatechopper

How do i do that...

- asnaseer

can you find the point of intersection of these two lines?

- asnaseer

just substitue y=-(1/3)x from 1st equation into 2nd equation and solve for x.

- asnaseer

then use 1st equation to find the y value once you have the x value

- karatechopper

Ah ok!

- karatechopper

So like....the answer would be for x=3?

- asnaseer

make sure you have the correct sign - does it look like x would be positive here?

- karatechopper

aahhhh!!! negative negative!!

- asnaseer

:)

- asnaseer

now find y value

- asnaseer

use the first equation for that, i.e. y = -(1/3)x to find y. remember you just found x=-3

- karatechopper

Oh i know i am working it out!!!

- karatechopper

y=19

- asnaseer

how???

- asnaseer

x=-3, therefore:\[y=-\frac{1}{3}\times x=-\frac{1}{3}\times (-3) = ?\]

- karatechopper

Oh ok i was using a dif equation.

- karatechopper

y=-1

- asnaseer

please be more careful in your calculations - try again...

- karatechopper

gAAAA

- karatechopper

Ohhhhhhhh y=1

- asnaseer

good. so now you know the point of intersection is (-3, 1):
|dw:1350952783534:dw|

- 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

Alright thanks!

- asnaseer

yw :)

- karatechopper

Now SLEEP! I am ordering my papa to sleep:)

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