SOLUTION: "Find three different ordered pairs that are solutions of the equation: 1. x=1/2" I don't understand how you can find an ordered pair for this without including the y. Can you

Question 694767: "Find three different ordered pairs that are solutions of the equation:
1. x=1/2"
I don't understand how you can find an ordered pair for this without including the y. Can you please help explain this to me?
Thank you so much in advance.
Found 2 solutions by Ave, RedemptiveMath:
Answer by Ave(106) (Show Source): You can put this solution on YOUR website!
If you were to graph the equation x=1/2 it would be a horizontal line that goes through every (1/2, y) point. You can replace any number with y and it would lay on that line.
(1/2, 1)
(1/2, 2)
(1/2, 3)
(1/2, 4)
and so on
Answer by RedemptiveMath(80) (Show Source): You can put this solution on YOUR website!
This problem may become clearer if we think of graphing. If x = 1/2 is an equation to a line in the Cartesian (rectangular) coordinate system, then we know that by graphing the slope is undefined and the vertical line of that graph passes through 1/2 on the x-axis. We know that no matter how high or how low you go on this line, the x-value will always read 1/2. By algebra, we know that the x-value must remain 1/2 (simplified) in order for the equation x = 1/2 to be true. Therefore, in ordered pairs the x-value will remain 1/2. This will satisfy algebra and graphing. Now the y-values may make this problem more confusing. Looking at the line and equation, we can think of two different paths of logic to take to justify our solutions.

Again, we know the line states that the x-value will always remain 1/2, but the y-value will change when we move on the graph. Logically, since x must remain 1/2 and y is going to change, our three solutions must have x as 1/2 and y as anything. The y-values in each of our three solutions must not repeat because that would mean we have used the same point over again. (If our three answers are (1/2, 9), (1/2, 5) and (1/2, 9), we have two answers that repeat and thus we only have two unique points. We must have three different points for our answer.) So, we could have answers as so:

(1/2, -13)
(1/2, 85)
(1/2, 1/2)
(1/2, "anything").

We can virtually plug anything (within reason) for y and satisfy the problem. This is because x must remain the same since the x-value of the line x = 1/2 never changes, and this is because the y-values can change if we go up or down. You may ask, "Looking at our equation, how is it that we can pick any y-value and satisfy the equation x = 1/2? Where do the y-values go?"

The second logical method we could use to prove our point is by looking at our equation an breaking it down. We've said before that x must remain 1/2 because the equation literally states "x is equal to 1/2." To answer the question about the y-values, I look at it like this: Since we've said that the y-value can be anything on the line x = 1/2, it would make things very complicated and complex to try to introduce every single y-value (even using the infinity notation) into an equation that can simply be written as "x = 1/2." This equation satisfies the idea that the x-value remains the same, and since the x-value remains the same the line graphed goes straight up and down. Since the line goes on forever unless otherwise directed, the positive and negative y-values are being represented by this line. That is, the line passes by (not through) parallel to every y-value in the Cartesian coordinate system. We have fixed point at x = 1/2, so the line can't pass through the y-axis without bending. However, it still represents every point on the y-axis. Therefore, we really only need to look at the x-value for an equation reading "x equals..." in order to find other solutions to that line (y can virtually be anything).

This is all explained with the idea that "x = 1/2" is an equation to a line in the Cartesian coordinate system, and that there are no other restrictions or opinions given by your teacher or course that I am unaware of.
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