# How to find the x and y-intercept given  2x-y=4?

May 18, 2015

The x-intercept is the point ${P}_{1} = \left(2 , 0\right)$ and the y-intercept is the point ${P}_{2} = \left(0 , - 4\right)$

Firstly, let's write your function in a standard form :

$2 x - y = 4 \implies y = 2 x - 4$

When you seek the x-intercept, there is one information you know : the $y$ value of the intercept, its ordinate $= 0$. Thus, you have a point $\left(x , y\right) = \left(x , 0\right)$.

You can now replace the $y$ in your equation with $0$ :

$0 = 2 x - 4 \implies 2 x = 4 \implies x = 2$

The x-intercept is the point ${P}_{1} = \left(2 , 0\right)$.

Same thing for the y-intercept except that the information you know is the $x$ value of the intercept, the ordinate, which is $= 0$.
Thus, your have a second point $\left(x , y\right) = \left(0 , y\right)$.

Let's replace the $x$ in the equation with $0$ :

$y = 2 \cdot 0 - 4 = - 4$.

The y-intercept is the point ${P}_{2} = \left(0 , - 4\right)$.

That's it.