Hidden in x-y Plane SightDate: 11/29/2011 at 23:28:19 From: Renee Subject: x=4 Why is this a vertical line? x = 4 I don't understand. Date: 11/30/2011 at 10:31:11 From: Doctor Ian Subject: Re: x=4 Hi Renee, Think about a line that isn't horizontal or vertical, like 2x + 3y = 8 A "solution" to any equation is an assignment of values to variables that makes the equation true. In this case, these values make the equation true: 2(1) + 3(2) = 8 So (x = 1, y = 2) is a solution to the equation. More simply, we might write just (1,2). Does this make sense so far? Now, for this line, every time we change x, we have to change y, too. For example, if we increase x to 2, we get 2(2) + 3y = 8 3y = 4 y = 4/3 So (2,4/3) is also a solution. But now think about this line: 0x + 2y = 8 Since the coefficient of x is zero, it doesn't matter what x is. As long as y is 4, we can choose any x, and it will be a solution. So (1,4), (5,4), (-6,4), and so on, are all solutions. If you graph those, you get a horizontal line. Make sense? Now, what if we have this? 2x + 0y = 6 In this case, as long as x is 3, we can choose any value for y. So (3,1), (3,-4), and (3,19.8) are all solutions. If you graph those, you'll get a vertical line. Make sense? Now, in the horizontal case, we can simplify the equation by noting that 0x is always 0, to get 2y = 8 So this kind of equation gives a horizontal line: you can't see the x term, 0x -- but it's implied. In the vertical case, we can simplify the equation by noting that 0y is always 0, to get 2x = 6 So this kind of equation gives a vertical line: you can't see the y term -- 0y, but it's implied. Does this all make more sense now? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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