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Math Help - Linear equation question

  1. #1
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    Arrow Linear equation question

    In the Standard form any Linear equation, y = ax + b, one of our exercises is to take a real world situation and plug in the numbers and solve for the root, or zero.

    My question is this. Is there a general rule, or guideline for explaining which of your known numbers into it's proper place in this equation?


    I know that "a" represents the change in the output, or the "y" variable


    I'm a little foggy on the others...

    Any help would be greatly appreciated!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mklangelo View Post
    In the Standard form any Linear equation, y = ax + b, one of our exercises is to take a real world situation and plug in the numbers and solve for the root, or zero.

    My question is this. Is there a general rule, or guideline for explaining which of your known numbers into it's proper place in this equation?


    I know that "a" represents the change in the output, or the "y" variable


    I'm a little foggy on the others...

    Any help would be greatly appreciated!!
    in y = ax + b

    y is the output

    x is the input

    a is the rate of change of the output (with respect to the input). that is, how y changes as we change x

    b is the y-intercept, which is basically the intial output if no (zero) input is given
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  3. #3
    Forum Admin topsquark's Avatar
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    I'll add a somewhat different "dictionary" to Jhevon's answer. The a term is often known as the "linear coefficient" (in this case it can also be called the "leading coefficient.") The b term can be called the "constant coefficient" or constant term.

    -Dan
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  4. #4
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    Thanks for that information.


    I'll use a problem we have worked on. It's all clear to me when it's explained as far as the formula goes, but I'm just a bit foggy on when your given a real world situation and knowing what numbers will represent the various parts of the formula.


    For instance if I want to hire an electrician and he charges 50.00/hour with a 35.00 trip charge. He charges the trip charge regardless of whether or not he works as all.


    So which parts of the equation would these numbers represent?



    y is 50?

    x is the number of hours?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mklangelo View Post
    Thanks for that information.


    I'll use a problem we have worked on. It's all clear to me when it's explained as far as the formula goes, but I'm just a bit foggy on when your given a real world situation and knowing what numbers will represent the various parts of the formula.


    For instance if I want to hire an electrician and he charges 50.00/hour with a 35.00 trip charge. He charges the trip charge regardless of whether or not he works as all.


    So which parts of the equation would these numbers represent?



    y is 50?

    x is the number of hours?
    if we have y = ax + b, where y = total charge, and x = number of hours, we have for this question, a = 50, and b = 35 (do you see why?)

    so we have y = 50x + 35

    when y = 50, we have:

    50 = 50x + 35

    and we simply solve for x to find the number of hours
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  6. #6
    Bar0n janvdl's Avatar
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     y = 50x + 35 I wanted to put the  50x over 60, but i realised he charges per hour, not minute.

    Heck, look at this graph, that guy sure pockets a lotta money!

    You can't see it too clearly, but the graph starts at 35 on the y-axis? Do you realise why?
    Attached Thumbnails Attached Thumbnails Linear equation question-electrician.jpg  
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  7. #7
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    So in this case, b is the y intercept or the initial output since that is where you will start. He gets his trip charge regardless. If he had not charged for the trip, the y intercept would have been (0,0).
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mklangelo View Post
    So in this case, b is the y intercept or the initial output since that is where you will start. He gets his trip charge regardless. If he had not charged for the trip, the y intercept would have been (0,0).
    correct. since he charges for the trip, when we have zero hours of work, we still pay $35, so when x = 0, y = 35, hence we have the point (0, 35) which is the y-intercept. in addition, he charges $50 per hour, so for x hours, he charges $50x, hence we have the 50x. y, the total charge, is the sum of these, thus, finally, we have y = 50x + 35, which is the line janvdl graphed for us
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  9. #9
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    Thank you for your time on this!


    By the way, this electrician is cheap...
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