# Gradient of Line **In general, why is it assumed there is only one line passing through two points with a given slope, rather than an infinite amount of overlapping lines?** A line in space is obtained by placing a ruler in space at some fixed point with a fixed direction, and drawing the line it gives. That is, every point of a line can be described in the form `x(t)=x0+tv𝑥(𝑡)=𝑥0+𝑡𝑣` where x0𝑥0 is the starting point in space, and t𝑡 is the "time it takes to get to x𝑥 in the direction of the velocity vector v𝑣." If a line given parametrically by `x(t)=x0+tv𝑥(𝑡)=𝑥0+𝑡𝑣` passes through P𝑃 and Q,𝑄, we may without loss of generality assume it passes through P𝑃 at time 0 and Q𝑄 at time 1--we may scale and/or shift t as necessary to accomplish this. So we have `x(t)=x0+tv𝑥(𝑡)=𝑥0+𝑡𝑣` `x(0)=P𝑥(0)=𝑃` `x(1)=Q𝑥(1)=𝑄` from which we conclude `x0=P𝑥0=𝑃` `v=Q−P.𝑣=𝑄−𝑃.` `That is, x(t)𝑥(𝑡) must given by` `x(t)=P+t(Q−P),𝑥(𝑡)=𝑃+𝑡(𝑄−𝑃),` and there is a unique line between P𝑃 and Q.\
Based on the well-established mathematical principle, we propose the following understanding: > **A straight line defined by two specific points can include infinitely many other points. This is because only one straight line can pass through any two fixed points.** For instance, consider a straight line named Line X that passes through two given points, A and B. If you choose any other two points on this line, say C and D, and remove the original points A, B, and Line X, you can still redraw the same straight line through points A and B using the new points C and D. By repeating this process, it becomes evident that a straight line contains infinitely many points. This concept is supported by mathematical proofs available on platforms like Math Stack Exchange. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://enerzion.gitbook.io/enerzion/introducing-enerzion/gradient-of-line.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.