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Math Help - Precalculus - Slopes

  1. #1
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    Precalculus - Slopes

    Find the slope m of the line in the following figure.


    Thanks for the help!
    Attached Thumbnails Attached Thumbnails Precalculus - Slopes-p.57-56.png  
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  2. #2
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    Let's use the form y=mx+c.
    Since the line passes through (2,1) we know 1=2m+c
    We also know that the y intercept is c and by substituting y=0 we can discover that the x intercept is -c/m. Using the formula for the area of a triangle, we get \frac12 (c)(\frac{-c}{m})=4. Then it is just a matter of solving the simultaneous equations.
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  3. #3
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    I'm sorry. I don't quite understand how to solve . Could you explain more, please?
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  4. #4
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    Quote Originally Posted by juicysharpie View Post
    Find the slope m of the line in the following figure.


    Thanks for the help!
    let eqn. of line be

    x/a+y/b=1-----------------------intercept formula

    since it passes through....(2,1)

    2/a+1/b=1 .................................................. ....(1)

    areaof triangle=4=1/2*ab

    ab=8.............................................. .................(2)

    solve these eqn. to find the values of a,b

    then find the slope m=b/a
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  5. #5
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    Question

    hmmm...I didn't learn that intercept formula. Is there another way to approach this problem?
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  6. #6
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    Let's use the form y=mx+c.
    Since the line passes through (2,1) we know 1=2m+c
    We also know that the y intercept is c and by substituting y=0 we can discover that the x intercept is -c/m. Using the formula for the area of a triangle, we get . Then it is just a matter of solving the simultaneous equations.
    \frac12 (c) (\frac{-c}{m}) = 4
    \implies \frac{-c^2}{m} = 8
    \implies m = -\frac{c^2}{8}
    substitute into 2m+c = 1

    <br />
2(-\frac{c^2}{8})+c = 1

    can you continue?
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  7. #7
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    Yes, I can. Thank you sooo much!

    Is the answer m = -1/2?
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  8. #8
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    Is the answer m = -1/2?
    Yes it is. Well done.
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