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Suppose y is directly proportinal to x

  1. May 5, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-5-5_12-33-17.jpeg


    Suppose that y is directly proportional to x. Show that y is a linear function of x. Both lines goes through the origin. First line goes 1250 ft in x direction and 50 ft in y direction. The second line goes 13740 ft in x direction and 920.58 ft in y direction.

    Source: Algebra and Trigonometry by Keedy/Bittinger.
    2. Relevant equations
    y=mx+n



    3. The attempt at a solution

    1.y=mx+n since line goes through the origin y-intercept is 0. We know y-intercept and slope then we can write a slope-intercept equation for the line. m=50/1250=0.04; y=0.04x

    2. y=mx+n since line goes through the origin y-intercept is 0. We know y-intercept and slope then we can write a slope-intercept equation for the line. m=0.067x

    But here I do not understand why the information "y is directly proportional to x" is given? What are other ways to solve this problem?

    Thank you.

     
  2. jcsd
  3. May 5, 2017 #2
    Its given cause its implies x is proportional to y. Like y=ax where a is a constant reel number this function like y=ax so f(x)=ax is a linear function.I dont think theres any other way to solve this question.
     
  4. May 5, 2017 #3
    Isn't y in y=x2directly proportinal to x?
     
  5. May 5, 2017 #4
    Its not
     
  6. May 5, 2017 #5

    DrClaude

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    Staff: Mentor

    If y is directly proportional to x, then doubling the value of x doubles the value of y.
     
  7. May 5, 2017 #6
    How is this square case of proportionality called?

    Thank you.
     
  8. May 5, 2017 #7

    DrClaude

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    Staff: Mentor

    "y is proportional to x squared"

    Mathematically, it is the difference between ##y \propto x## and ##y \propto x^2##.
     
  9. May 5, 2017 #8

    Ray Vickson

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    Science Advisor
    Homework Helper

    ##y## proportional to ##f(x)## just means that ##y/f(x)## is a constant; that is, ##y = c f(x)## for some constant ##c##.
     
  10. May 5, 2017 #9

    CWatters

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    What's with the question numbers (50,51,52)? Is 50 referring to 51 and 52?
     
  11. May 5, 2017 #10
    I think 50 is the question and 51 and 52 are parts of it. That's all in the picture.

    Thank you.
     
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