As you’ve just seen, you need to know both the x-coordinate and the y-coordinate to plot a point exactly on the coordinate plane. If you only know one coordinate, you can’t tell precisely where the point is, but you can narrow down the possibilities.
Consider this situation. Say that this is all you know: the point is 4 units to the right of 0:
As you saw earlier, any point along the vertical dotted line is 4 units to the right of 0. In other words, every point on the dotted line has an x-coordinate of 4. You could shorten that and say x = 4. You don’t know anything about the y-coordinate, which could be any number. All the points along the dotted line have different y-coordinates but the same x-coordinate, which equals 4.
So, if you know that x = 4, then your point can be anywhere along a vertical line that crosses the x-axis at (4, 0). Try another example.
If you know that x = −3…
Then you know...
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Every point on the dotted line has an x-coordinate of −3. |
Points on the dotted line include (–3, 1), (–3, –7), (–3, 100), and so on. In general, if you know the x-coordinate of a point and not the y-coordinate, then all you can say about the point is that it lies somewhere on a vertical line.
The x-coordinate still indicates left-right position. If you fix that position but not the up-down position, then the point can only move up and down—forming a vertical line.
Now imagine that all you know is the y-coordinate of a number. Say you know that y = −2. How could you represent this on the coordinate plane? In other words, what are all the points for which y = –2?
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Every point 2 units below 0 fits this condition. These points form a horizontal line. You don’t know anything about the x-coordinate, which could be any number. All the points along the horizontal dotted line have different x-coordinates but the same y-coordinate, which equals −2. For instance, (−3, −2), (−2, −2), and (50, −2) are all on the line. |
Try another example. If you know that y = 1…
Then you know...
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Every point on the dotted line has a y-coordinate of 1. |
If you know the y-coordinate but not the x-coordinate, then you know the point lies somewhere on a horizontal line.
Draw a coordinate plane and plot the following lines.
x = 6
y = −2
x = 0