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I have a very basic question but I can not wrap my head around it.

We use this formula for the equation of a straight line:

$$Ax + By = Ax_0 + By_0$$

Where $A$ and $B$ are the $x$ and $y$ coordinates of a normal vector and $x_0$ and $y_0$ are coordinates of a given point on the line.

$$\begin{array}{c} \mathbf n(A;B)\\ P(x_0;y_0)\end{array}$$

Usually we have something like:

$$2x-3y = 7$$

And we know that the coordinates of this line's normal vector are $2$ and $-3$.

But now, I have this linear equation:

$$ x-8.4 = 0$$

How do I get the coordinates of this line's normal vector as there is no $Y$ value?

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    Use MathJax for mathematical expressions, not code blocks. – 2017-02-18

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What if you wrote it as $1x + 0y = 8.4$

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    Thanks! But why isn't the normal vector (0 ; 8.4)? – 2017-02-17
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    @BalázsVincze Why isn’t the normal vector $(3,7)$ in your first example? – 2017-02-17
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    @amd I edited my question to clarify a bit! – 2017-02-17
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    @BalázsVincze Draw the line: it’s vertical (parallel to the $y$-axis). Any vector of the form $(0,y)$ is *parallel* to this line, not normal to it. In your own terms, the $8.4$ is the $\mathbf n\cdot P$ part of the equation. – 2017-02-18