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Thread: Finding equation for a line?

  1. #1
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    Finding equation for a line?

    I don't even know to to start on this problem. It doesn't even give you any coordinates at all so how am I suppose to find the equation for this line?

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  2. #2
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    Well the equation of a line in this case can be given by $\displaystyle y = mx+c$

    They have told you that $\displaystyle m= 4$ so $\displaystyle y = 4x+c$

    They have also told you the line shares a point with the parabola. This point is $\displaystyle (2, 2^2) = (2,4)$ so

    $\displaystyle 4 = 4\times 2+c$

    Now solve for $\displaystyle c$ and your done.
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  3. #3
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    Use the form $\displaystyle y=mx+b$

    m is slope
    b is y intercept

    m=4 (given)

    Put in the equation:
    $\displaystyle y=4x+b$
    We are given in the graph a point x=2 there is an interception with the graph $\displaystyle y=x^2$
    so $\displaystyle y=(2)^2$ or $\displaystyle y=4$ at that point.

    Now you know the point (2,4) is on the graph.

    put in 2 for x and 4 for y in the $\displaystyle y=4x+b$ and solve for b:

    $\displaystyle y=mx+b$
    $\displaystyle 4=4*2+b$
    $\displaystyle b=1/2$

    now you are done!
    $\displaystyle y=4x+.5$
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  4. #4
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    Nevermind snaes answered my question. Thank you so much for helping me with this question!

    I just got the answer and it is y = 4x -4. I think you kind of got it mixed up snaes.
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  5. #5
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    correct.
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  6. #6
    Super Member bigwave's Avatar
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    also another way to get

    $\displaystyle y = mx+c$

    is to use the point slope form
    $\displaystyle y-y_1 = m(x - x_1)$

    so using point x = 2 and since y=2^2 = 4 with have the point (2,4)

    then

    $\displaystyle y-4 = 4(x-2) $
    $\displaystyle y = 4x - 8 +4$
    $\displaystyle y = 4x -4$
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  7. #7
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    Quote Originally Posted by snaes View Post

    $\displaystyle y=mx+b$
    $\displaystyle 4=4*2+b$
    $\displaystyle b=1/2$

    now you are done!
    $\displaystyle y=4x+.5$
    This is not correct.
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  8. #8
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    Thank you so much for your help guys I really appreciate it. Now I am stuck on this problem. How would I find out the slope of it? I already plugged in the x and y intercepts it gave me into the equation y = x^2 + 1 and got the coordinate (square root of 7, 5). I'm thinking the top of the triangle is 10 and the right side might be 1 but I'm not quite sure. So that makes it a rise over run of 1/10. Is that the correct slope?

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  9. #9
    Super Member bigwave's Avatar
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    you have to do the rise/run based on the 2 points

    first find the (x,y) of the 2 intersecting points

    then use $\displaystyle m = \frac{y-y_1}{x-x_1}$ for the slope

    as you have found

    $\displaystyle Q(2,5)$ and $\displaystyle P(\sqrt{7},8)$

    then

    $\displaystyle m = \frac{8-5}{\sqrt{7}-2}$

    then just simplify

    I got $\displaystyle m=\sqrt{7} + 2 $ but double check this
    Last edited by bigwave; Feb 1st 2010 at 09:29 PM. Reason: wording
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  10. #10
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    I don't think that is the right answer. Here's what it says in the back of the book:

    At this time I got the slope 3/sqrt{7} - 2 and is trying to plug in (2,5) into the equation y = mx + b. But I get stuck at this point 5 = 3/sqrt{7} - 2 (2) + b
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  11. #11
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    Quote Originally Posted by bigwave View Post
    $\displaystyle m = \frac{8-5}{\sqrt{7}-2}$

    then just simplify

    I got $\displaystyle m=\sqrt{7} + 2 $ but double check this
    Ray (Bigwave) has rationalised the denominator to get $\displaystyle m=\sqrt{7} + 2 $

    i.e. $\displaystyle m = \frac{3}{\sqrt{7}-2}\times \frac{\sqrt{7}+2}{\sqrt{7}+2}=\sqrt{7} + 2$

    It is not required in this case.
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  12. #12
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    Thanks so much for helping me with this problem.
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