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Why is the graph for x=3 (Or C where C is a constant) as a vertical line on the xy coordinate plane or Y = some C as a horizontal line? Shouldn’t they be points?

Nicko Cruz M
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    Because for every value of $x$ we have a point $(x,C)$ in the xy-graph. – Mauro ALLEGRANZA Nov 17 '22 at 10:34
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    When you plot a function $f$ you generate all values $f(a)$ of the function for input value $a$. The plot is the graph of points $(a,f(a))$. – Mauro ALLEGRANZA Nov 17 '22 at 10:39
  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Nov 17 '22 at 10:49
  • They are points: the graph of x=c is obtained by plotting each possible point in which abscissa equals c; the graph of y=c is obtained by plotting each possible point in which ordinate equals c. Plot 10 points in each case. What you will get if you plot all possible points? – Pedro Nov 17 '22 at 10:55

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This comes to the interpretation of Cartesian equations. The graph $(C)$ of equation $f(x, y)=0$ is by definition the set $$ \{ (x,y)\in\mathbb{R}^2| f(x,y)=0\} $$

In particular, the graph of $x=c$ is the set $\{(x, y)|x=c\}=\{(c, y)|y\in\mathbb{R}\}$ , The case of $y=c$ is analogous.

On a more intuitive level, a point in 2D space (the plane) has 2 degrees of freedom (corresponding to its two coordinates), fixing one of them only takes one degree of freedom which means that the resulting space should be 1-dimensional rather than 0-dimensional.

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