Although not in it's best form, it does describe a line, yes. A more classic way to write it would be:
y = x
So the line in question would be a perfect diagonal, with a slope of 1 which intersects the point 0, 0.
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y = 2x + 1 IS a linear equation!
Yes.
yes
Yes.
It appears to be a simple linear equation in 'x'. But it has no solution. There is no numerical value for 'x' that can make it a true statement.