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karatechopper

  • 3 years ago

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

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  1. zonazoo
    • 3 years ago
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    the vertical distance, or horizontal distance or what?

  2. karatechopper
    • 3 years ago
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    |dw:1350957364620:dw|

  3. zonazoo
    • 3 years ago
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    that perpendicular line between the two is the distance you want?

  4. asnaseer
    • 3 years ago
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    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.

  5. asnaseer
    • 3 years ago
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    Hope that makes sense?

  6. zonazoo
    • 3 years ago
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    yeah, thats what i would do

  7. karatechopper
    • 3 years ago
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    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?

  8. asnaseer
    • 3 years ago
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    ok, step 1 - do you know the relationship of the slopes of two lines that are perpendicular to one another?

  9. karatechopper
    • 3 years ago
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    I know that the perpendicular slope is the opposite reciprocal of the slope.

  10. asnaseer
    • 3 years ago
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    almost - the product of the slopes of two perpendicular lines is always -1.

  11. asnaseer
    • 3 years ago
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    so - what would be the slope of the line that is perpendicular to y=3x?

  12. karatechopper
    • 3 years ago
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    -1/3x

  13. asnaseer
    • 3 years ago
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    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

  14. asnaseer
    • 3 years ago
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    agreed?

  15. karatechopper
    • 3 years ago
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    Correct. I got that part.

  16. asnaseer
    • 3 years ago
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    good, now if we take this perpendicular line such that it passes through the origin, then what would be the value for c?

  17. asnaseer
    • 3 years ago
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    remember we have: y = -(1/3)x + c and we know y=0 when x=0, therefore c=?

  18. asnaseer
    • 3 years ago
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    are you stuck?

  19. karatechopper
    • 3 years ago
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    yes..

  20. karatechopper
    • 3 years ago
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    C=0

  21. asnaseer
    • 3 years ago
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    yes - correct

  22. karatechopper
    • 3 years ago
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    Yay!

  23. asnaseer
    • 3 years ago
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    so now we know that the line perpendicular to y=3x and that passes through the origin has the equation: y = -(1/3)x

  24. karatechopper
    • 3 years ago
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    Ok, so i drew that line in on my graph..

  25. karatechopper
    • 3 years ago
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    |dw:1350958743362:dw|

  26. asnaseer
    • 3 years ago
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    |dw:1350951532761:dw|

  27. karatechopper
    • 3 years ago
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    Yea! That!

  28. asnaseer
    • 3 years ago
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    so next you want to find the point of intersection of: y = -(1/3)x and: y = 3x + 10

  29. karatechopper
    • 3 years ago
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    Oh ok !

  30. karatechopper
    • 3 years ago
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    How do i do that...

  31. asnaseer
    • 3 years ago
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    can you find the point of intersection of these two lines?

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

  33. asnaseer
    • 3 years ago
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    then use 1st equation to find the y value once you have the x value

  34. karatechopper
    • 3 years ago
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    Ah ok!

  35. karatechopper
    • 3 years ago
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    So like....the answer would be for x=3?

  36. asnaseer
    • 3 years ago
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    make sure you have the correct sign - does it look like x would be positive here?

  37. karatechopper
    • 3 years ago
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    aahhhh!!! negative negative!!

  38. asnaseer
    • 3 years ago
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    :)

  39. asnaseer
    • 3 years ago
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    now find y value

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

  41. karatechopper
    • 3 years ago
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    Oh i know i am working it out!!!

  42. karatechopper
    • 3 years ago
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    y=19

  43. asnaseer
    • 3 years ago
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    how???

  44. asnaseer
    • 3 years ago
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    x=-3, therefore:\[y=-\frac{1}{3}\times x=-\frac{1}{3}\times (-3) = ?\]

  45. karatechopper
    • 3 years ago
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    Oh ok i was using a dif equation.

  46. karatechopper
    • 3 years ago
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    y=-1

  47. asnaseer
    • 3 years ago
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    please be more careful in your calculations - try again...

  48. karatechopper
    • 3 years ago
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    gAAAA

  49. karatechopper
    • 3 years ago
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    Ohhhhhhhh y=1

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

  51. asnaseer
    • 3 years ago
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    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.

  52. karatechopper
    • 3 years ago
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    Alright thanks!

  53. asnaseer
    • 3 years ago
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    yw :)

  54. karatechopper
    • 3 years ago
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    Now SLEEP! I am ordering my papa to sleep:)

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