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Math Help - Challenging slope, point problem I need help with.

  1. #1
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    Challenging slope, point problem I need help with.

    So just registered, and was hoping you guys and girls could help me this problem. I have never encountered one like it.

    Here it is:

    Find the slope of all lines through (7,-4) whose slope is half of its x-intercept.

    I would appreciate if anyone could help me. Thanks!
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  2. #2
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    Re: Challenging slope, point problem I need help with.

    Hey mathgeek04.

    Hint: The equation of a straight line is y = mx + b = y - y0 = m(x - x0) where (x0,y0) is a point on the line.
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  3. #3
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    Re: Challenging slope, point problem I need help with.

    Quote Originally Posted by chiro View Post
    Hey mathgeek04.


    Hint: The equation of a straight line is y = mx + b = y - y0 = m(x - x0) where (x0,y0) is a point on the line.
    Just to clarify: Those are not all equal... y = mx + b is the slope-intercept form of the line. y-y_0 = m(x - x_0) is the point-slope form of a line. But, mx + b does not equal y - y_0 unless y_0 = 0.

    Edit: Since you are given a point, I would recommend using point-slope form for the line.
    Last edited by SlipEternal; November 13th 2013 at 04:35 PM.
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  4. #4
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    Re: Challenging slope, point problem I need help with.

    I understand what slope-intercept form is and I understand what point-slope form is, but what do I do with that?
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  5. #5
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    Re: Challenging slope, point problem I need help with.

    Do you know what an x-intercept is?
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    Re: Challenging slope, point problem I need help with.

    Quote Originally Posted by SlipEternal View Post
    Do you know what an x-intercept is?
    Yes, it is the point where y is 0 so it it (x,0)
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  7. #7
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    Re: Challenging slope, point problem I need help with.

    Exactly. So, write out the equation for a line in point-slope form (with the point you are given). The x-intercept for the line will be (2m,0) (since the problem tells you the slope is half of the x-intercept). Use that. Plug in y=0, x=2m and solve for m.
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  8. #8
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    Re: Challenging slope, point problem I need help with.

    Thanks for clearing that up, but I do hope it was obvious what was meant to be conveyed.
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  9. #9
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    Re: Challenging slope, point problem I need help with.

    Quote Originally Posted by SlipEternal View Post
    Exactly. So, write out the equation for a line in point-slope form (with the point you are given). The x-intercept for the line will be (2m,0) (since the problem tells you the slope is half of the x-intercept). Use that. Plug in y=0, x=2m and solve for m.
    Okay so,

    y+4=m(2m-7)
    4=2m^2-7m
    2m^2-7m-4=0
    m=4 and m=-0.5

    Is that correct?
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  10. #10
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    Re: Challenging slope, point problem I need help with.

    Correct. So, the two lines are:

    y+4 = 4(x-7)

    and

    y+4 = -0.5(x-7)
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  11. #11
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    Re: Challenging slope, point problem I need help with.

    Quote Originally Posted by SlipEternal View Post
    Correct. So, the two lines are:

    y+4 = 4(x-7)

    and

    y+4 = -0.5(x-7)

    Thank you, so much!
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