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I encountered the following claim on a website:

Geometrically, a plane is just a linear object in more than two dimensions. A line is, of course, a linear object in two dimensions. And linear means that it has constant slope (in each direction).

This makes no sense to me. A plane is clearly a two-dimensional object, and a line is a one-dimensional object. But this excerpt says that a plane is a linear object in more than two dimensions, and a line is a linear object in two dimensions? What does this mean and how is it different from my understanding?

I would greatly appreciate it if people could please take the time to clarify this and elaborate.

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    The Web, like Esope's tongue, is the best and the worst thing. In this case it is the worst. This is nonsense : a plane is two dimensional, a line is one dimensional, an hyperplane is $n-1$ dimensional. The reference to "slope" is also to be forgotten... – 2017-02-26
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    It's pretty much impossible to clarify and elaborate a two sentence out-of-context quote. But I will say that the word "linear" has a wider mathematical meaning that its close relation to the word "line" might suggest. A close study of linear algebra, and particularly the concept of a linear transformation between vector spaces, will exhibit this wider meaning. – 2017-02-26

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