Writing the equation of a straight line parallel to the $y$-axis

Question

I know that the general equation for a line is $y=mx+n$, where $m$ is the slope and $n$ is the value of $y$ when $x=0$. I was wondering how would you write the equation for a vertical line with the equation $(x=c)$ so that we have something of the $y=\text{ something}$ shape.

Answer 1

If $a$ is the $x$-intercept of a straight line parallel to the $y$-axis, note that the equation of the line is then given by $$x = a.$$

Can you figure out why?

(Hint: A straight line parallel to the $y$-axis must be a vertical line.)

Answer 2

you can't write a line equation which is parallel to the $y$ axis as an equation of the form: $y = mx+n$, because for every two points on the line, if you will try to find the slope, you'll find that for every two points on this line (or every line parallel to the $y$ axis): $m=\frac{x_2-x_1}{y_2-y_1}=\frac{x_2-x_1}{0}$, hence $m \to \infty$.

Answer 3

One can think of the equation of a line as a tool to select a whole set of points , that is a set of couples (x,y) in the plane.

This selecting tool generally states a relation between y and x. If you want to select all points (x,y) such that y is twice as big as x, you write : $y=2x$.

Now, you may only express a requirement as to x, while not caring about y. In that case you can write : $x= 5$ for example.

What you will select will be the set of all points (x,y) such that x=5 no matter what y is, that is, a line that is parallel to the Y axis and that lies 5 units to the right of it.

All the points of this line will satisfy the condition you have imposed.