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NoahsArk

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- TL;DR Summary
- Help understanding the concept of representing a line in this way.

I am having trouble with the concept that the equation L = {x + tv} is the more general form of the more familiar y = mx + b (In the first equation there should be a vector sign above the x and the v). It's hard for me to see the similarities between these two equations.

1: Even if we are dealing with a 2d space like y = mx + b lies in, in the equation L = {x + tv} we are dealing with the addition of two vectors (which I visualize as two line segments), whereas in y = mx + b we are only dealing with one line.

2: In y = mx + b, we are dealing with a relationship between y and x whereas in L = {x + tv} we are defining a line.

3: The comparison becomes even harder to grasp when we go beyond 3d space. How can we even call something a line that has more than three dimensions? Any conceptual explanation about what L = {x + tv} means would be helpful. I understand that y = mx + b represents a relationship between two variables and how one variable changes as the other changes, but I am not sure what L = {x + tv} is trying to show.

Thanks!

1: Even if we are dealing with a 2d space like y = mx + b lies in, in the equation L = {x + tv} we are dealing with the addition of two vectors (which I visualize as two line segments), whereas in y = mx + b we are only dealing with one line.

2: In y = mx + b, we are dealing with a relationship between y and x whereas in L = {x + tv} we are defining a line.

3: The comparison becomes even harder to grasp when we go beyond 3d space. How can we even call something a line that has more than three dimensions? Any conceptual explanation about what L = {x + tv} means would be helpful. I understand that y = mx + b represents a relationship between two variables and how one variable changes as the other changes, but I am not sure what L = {x + tv} is trying to show.

Thanks!

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