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

Feb 5, 2015

The x intercept is 6

$2 x + 3 y = 12$

At the $x$ intercept $y = 0$

So

$2 x + 0 = 12$

$x = \frac{12}{2} = 6$

Feb 5, 2015

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 $2 x + 3 \setminus \cdot 0 = 12$, which means $2 x = 12$, which yelds $x = 6$.

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