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Question 945091: If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a real-life situation where a graph would have no x- or y-intercept. Will what you say about the line always be true in that situation?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If a straight (endless) line (in a 2-dimensional x-y space) has no y-intercept,
a math teacher would call it a "vertical line",
meaning that it is parallel to the y-axis.
If a straight line (in a 2-dimensional x-y space) has no x-intercept,
a math teacher would call it a "horizontal line",
meaning that it is parallel to the x-axis.
Think of a real-life situation where a graph would have no x- or y-intercept?
Interesting question. I am trying to read the mind of whoever thought of that question.
In a 2-dimensional x-y space (like a piece of paper or a computer screen),
I can think of a real-life situation where a graph would have no x- or y-intercept.
It could be a curved line that would stay in one of the quadrants,
it could be a circle, for example,
or maybe a set of separate lines or points.
It could look like this  or this  , or maybe a set of separate line segments or points.
What would always be true in any such situation I can think of?
It is either a curved closed graph, or it is not a continuous graph.
I do not know what situation your teacher is thinking of, so I do not know what would always be true in that situation.
In a 3-dimensional space, I can also think of a straight line, an endless, continuous straight line, with no x-axis or y-axis intercept (and maybe not even a z-axis intercept).
In that case, I would say it is parallel to the x-y plane (always).
Could that be the situation your teacher is thinking of?
I can picture a segment of such a line as an almost real-life clothesline extending horizontally from one wall to another wall in a basement. One corner of the basement floor is the origin of my set of x-y-z coordinates.
(It is a mass-less line, so it is perfectly straight; it does not sag).
Two edges of the floor ending in that corner are segments of the x- and y-axes.
A line where two walls meet (the one ending in that corner) is a segments of the z-axis.
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