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karatechopper Group Title

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

  • 2 years ago
  • 2 years ago

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  1. zonazoo Group Title
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    the vertical distance, or horizontal distance or what?

    • 2 years ago
  2. karatechopper Group Title
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    |dw:1350957364620:dw|

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

    • 2 years ago
  4. asnaseer Group Title
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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.

    • 2 years ago
  5. asnaseer Group Title
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    Hope that makes sense?

    • 2 years ago
  6. zonazoo Group Title
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    yeah, thats what i would do

    • 2 years ago
  7. karatechopper Group Title
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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?

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

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

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

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

    • 2 years ago
  12. karatechopper Group Title
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    -1/3x

    • 2 years ago
  13. asnaseer Group Title
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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

    • 2 years ago
  14. asnaseer Group Title
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    agreed?

    • 2 years ago
  15. karatechopper Group Title
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    Correct. I got that part.

    • 2 years ago
  16. asnaseer Group Title
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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?

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

    • 2 years ago
  18. asnaseer Group Title
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    are you stuck?

    • 2 years ago
  19. karatechopper Group Title
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    yes..

    • 2 years ago
  20. karatechopper Group Title
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    C=0

    • 2 years ago
  21. asnaseer Group Title
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    yes - correct

    • 2 years ago
  22. karatechopper Group Title
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    Yay!

    • 2 years ago
  23. asnaseer Group Title
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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

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

    • 2 years ago
  25. karatechopper Group Title
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    |dw:1350958743362:dw|

    • 2 years ago
  26. asnaseer Group Title
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    |dw:1350951532761:dw|

    • 2 years ago
  27. karatechopper Group Title
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    Yea! That!

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

    • 2 years ago
  29. karatechopper Group Title
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    Oh ok !

    • 2 years ago
  30. karatechopper Group Title
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    How do i do that...

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

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

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

    • 2 years ago
  34. karatechopper Group Title
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    Ah ok!

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

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

    • 2 years ago
  37. karatechopper Group Title
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    aahhhh!!! negative negative!!

    • 2 years ago
  38. asnaseer Group Title
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    :)

    • 2 years ago
  39. asnaseer Group Title
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    now find y value

    • 2 years ago
  40. asnaseer Group Title
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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

    • 2 years ago
  41. karatechopper Group Title
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    Oh i know i am working it out!!!

    • 2 years ago
  42. karatechopper Group Title
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    y=19

    • 2 years ago
  43. asnaseer Group Title
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    how???

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

    • 2 years ago
  45. karatechopper Group Title
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    Oh ok i was using a dif equation.

    • 2 years ago
  46. karatechopper Group Title
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    y=-1

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

    • 2 years ago
  48. karatechopper Group Title
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    gAAAA

    • 2 years ago
  49. karatechopper Group Title
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    Ohhhhhhhh y=1

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

    • 2 years ago
  51. asnaseer Group Title
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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.

    • 2 years ago
  52. karatechopper Group Title
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    Alright thanks!

    • 2 years ago
  53. asnaseer Group Title
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    yw :)

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

    • 2 years ago
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