Parallel AsymptotesBy definition, any lines that are not parallel will intersect eventually. But to be...
Haley Madden
Answered
2022-07-21
Parallel Asymptotes
By definition, any lines that are not parallel will intersect eventually. But to be parallel lines, both lines must have the same slope. However, consider this situation:
There is a exponential graph that is an asymptote on the y-axis and on the same graph there is a reflection across the y-axis of the first exponential curve.
Now, we know that since these lines are asymptotes they will never actually reach the y-axis (where they would intersect). But also, they do not have the same slope. So - my question is - are these lines parallel?
By definition, any lines that are not parallel will intersect eventually. But to be parallel lines, both lines must have the same slope. However, consider this situation:
There is a exponential graph that is an asymptote on the y-axis and on the same graph there is a reflection across the y-axis of the first exponential curve.
Now, we know that since these lines are asymptotes they will never actually reach the y-axis (where they would intersect). But also, they do not have the same slope. So - my question is - are these lines parallel?
Answer & Explanation
le1kabp
Expert
2022-07-22Added 11 answers
Your definition that says "lines that never meet are parallel" is using "line" is a different way than you are. That definition is referring to a straight line in a 2-D Euclidean geometry, which the graph of your function is not.
To avoid this confusion, the graph of a function is often called a "curve" and only called a "line" when it happens to be straight.
To avoid this confusion, the graph of a function is often called a "curve" and only called a "line" when it happens to be straight.
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