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Could someone explian to me why the line x=4 is a vertical line

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suppose I have an equation like
x + y = 7

it states a relationship between the x and y that I choose, so that their sum is always 7
so I could have (1,6), (3,4), (10,-3) etc

now you gave me x = 4, there is no mention of y, so there is no restriction on y.
in other words, the y can be anything

wouldn't the following work?
(4,1), (4,4,), (4,-2) ??
your equation basically said, "my x must be 4, I don't care about anything else"

plot the points I gave you and see what you get.

BTW, could you now explain why
y = 5 would be a horizontal line?
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