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Math Help - slope on a simple graph

  1. #1
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    slope on a simple graph

    i have a given point of (3,2)
    i know that the slope is 2 and if i move two up i will have y equals 4
    but why should i move 1 to the right?
    the slope is 2 so i will move to up but why 1 to the right which leads to (4,4)?
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  2. #2
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    Re: slope on a simple graph

    The slope is the ratio of the vertical change to the horizontal change. When the slope of a line is 2 and (x, y) is on the line, then for any number z the point (x + z, y + 2z) is again on the line. Here the vertical change from (x, y) to (x + z, y + 2z) is 2z and the horizontal change is z.
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  3. #3
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    Re: slope on a simple graph

    why do you move on the x axis
    i take it from what you said that the slope indicates to move two up and one to the right
    why not just two up considering the slope is a standalone 2?
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  4. #4
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    Re: slope on a simple graph

    Quote Originally Posted by ariel32 View Post
    why do you move on the x axis
    i take it from what you said that the slope indicates to move two up and one to the right
    why not just two up considering the slope is a standalone 2?
    slope is \frac{\text{change in }y}{\text{change in }x}
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  5. #5
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    Re: slope on a simple graph

    If a line is sloped, then to move along the line and stay on it you need to move along both the y- and x-axes. The slope of the line is by definition the ratio of those displacements. If you move strictly up, then you leave the line.
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  6. #6
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    Re: slope on a simple graph

    if i may ask why did you decide to move just 1 on the x axis and while i am at it why did you move 2 up the y axis?
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  7. #7
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    Re: slope on a simple graph

    Quote Originally Posted by ariel32 View Post
    if i may ask why did you decide to move just 1 on the x axis
    I never decided this. I never mentioned the number 1 in my posts.

    Quote Originally Posted by ariel32 View Post
    and while i am at it why did you move 2 up the y axis?
    If you move 1 along the x-axis, then, in order to stay on the line, you need to move (the slope) * 1 = 2 * 1 = 2 along the y-axis. This is the definition of slope.
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  8. #8
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    Re: slope on a simple graph

    so if the slope was 4 i would move 1 to the right and 4 up?
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  9. #9
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    Re: slope on a simple graph

    Correct! Or 2 to the right and 8 up and so on.
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  10. #10
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    Re: slope on a simple graph

    i understand more now
    i suppose you have to move 1 to the right so that the run principle is met
    but why move 2 up and not 1 up?
    if you move 1 up you would still have a new point?
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  11. #11
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    Re: slope on a simple graph

    Quote Originally Posted by ariel32 View Post
    if you move 1 up you would still have a new point?
    Yes, but this point would not be on the line.
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  12. #12
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    Re: slope on a simple graph

    ok one final remark on the matter then.
    if you say that going 1 to the right means going 2 up by definition i would expect that going 10 to the right would not change the definition of the slope and expect to go only 2 up in such case or is the rule based differently?
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  13. #13
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    Re: slope on a simple graph

    Quote Originally Posted by ariel32 View Post
    if you say that going 1 to the right means going 2 up by definition i would expect that going 10 to the right would not change the definition of the slope and expect to go only 2 up in such case or is the rule based differently?
    Quote Originally Posted by emakarov View Post
    The slope is the ratio of the vertical change to the horizontal change. When the slope of a line is 2 and (x, y) is on the line, then for any number z the point (x + z, y + 2z) is again on the line. Here the vertical change from (x, y) to (x + z, y + 2z) is 2z and the horizontal change is z.
    If you move z = 10 to the right, then you need to move 2z = 20 up to stay on the line.
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