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Is it y-intercept?

  1. Jun 14, 2014 #1
    1. The problem statement, all variables and given/known data

    A crop dusting airplane flying a constant speed of 120 mph is spotted 2 miles South and 1.5 miles East of the center of a circular irrigated field. The irrigated field has a radius of 1 mile. Impose a coordinate system as pictured, with the center of the field the origin (0,0). The flight path of the duster is a straight line passing over the labeled points P and Q. Assume that the point Q where the plane exits the airspace above the field is the Western-most location of the field. Answer these questions:

    1. Find a linear equation whose graph is the line along
    which the crop duster travels.

    2. Relevant graph

    8xQMv3u.png

    3. The attempt at a solution

    The problem is just an example given in the textbook, and here's their solution:

    1. Take Q = (−1, 0) and S = (1.5,−2) = duster spotting point. Construct a line through Q and S. The slope is −0.8 = m and the line equation becomes:
    y = −0.8x − 0.8


    And my question is where did this y = −0.8x − 0.8 come from? Is it y-intercept? I'd assume it should be maybe: y = −0.8x − 2
     
  2. jcsd
  3. Jun 14, 2014 #2

    SteamKing

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    What is the value of y in your equation when x = 0? Does this equation match then match the diagram?

    Do you know how to find the y-intercept of a linear equation?
     
  4. Jun 14, 2014 #3

    LCKurtz

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    @maxpancho: You have two points given on the line, ##(-1,0)## and ##(\frac 3 2, -2)##. Do you know how to write the equation of a straight line through two given points? Try it and see what you get.
     
  5. Jun 15, 2014 #4
    Well, okay. So it's like I find b by taking a point (0,b) and then plug it into the origial equation. But that's what initially confused me click ...that they used y1 as it is.

    But I think I understand now. It's just another way of writing an equation of a line. In the first example it is written in a slope-intercept form, which is y = mx + b. And thus here we must first find the y-intercept m and then plug it back into the original equation.

    And in the second example it is written in a point-slope formula y = m(x − x1) + y1. Because I guess it is more convenient in this case, since m here would equal −2168140,17647058... But the equation is still valid, just not very practical.

    So I figure I could write the equation from the initial example as: y = −0.8(x − 1.5) − 2, which gives the same y = −0.8x −0.8 (oh wait, so then there was no need to plug 0,b trying to find m)...



    Is it correct?
     
    Last edited: Jun 15, 2014
  6. Jun 15, 2014 #5

    haruspex

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    Check whether it gives the right answer for two different values of x. If it does, it must be right.
     
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