Question

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

Answer 1

The x-intercept is the point `P_1= (2, 0)` and the y-intercept is the point `P_2 = (0, -4)`

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

`2x-y=4 => y=2x-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 `(x, y) = (x, 0)`.

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

`0 = 2x - 4 => 2x = 4 => x = 2`

The x-intercept is the point `P_1 = (2, 0)`.

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 `(x, y) = (0, y)`.

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

`y = 2*0 - 4 = -4`.

The y-intercept is the point `P_2 = (0, -4)`.

That's it.