Question

What is the x intercept of `2x+3y=12`?

Answer 1

The x intercept is 6

`2x+3y=12`

At the `x` intercept `y=0`

So

`2x+0=12`

`x=12/2=6`

Answer 2

This is the equation of a line, and thus there are of course infinite points which satisfy the equation, as a line has infinite point.

Fixing a `x` value, or a `y` value, means to fix a vertical, or a horizontal line, which will have only one intersection with your line.

This means that, if a line has obviously infinite point, it has anyway only one intersecating every vertical/horizontal line.

In our case, the `x` intercept is the intersection of your line with the `x` axis, which is nothing but a particular horizontal line, with `y` fixed to 0.

To find out the `x` intercept you have to plug `y=0` in the equation of the line, and find the only `x` that solves the equation.

In your case, we have `2x+3\cdot 0=12`, which means `2x=12`, which yelds `x=6`.

We have just proven that the point `(6,0)` belongs to the line, and since this is a point of the `x` axis, it is the line's `x` intercept.