Question

How do you find the x and y intercepts for `4x-2y=8`?

Answer 1

Rearrange into the form `y=mx+c` and substitue it `x` and `y` values of 0.

Explanation:

Rearrange into the form `y=mx+c`

To rearrange into the form `y=mx+c` we need to get `y` on its own. To do this we can take `4x` away from both sides to get:

`-2y = 8-4x`

Next we'll multiply both sides by -1 to flip the signs:

`2y = 4x-8`

Finally we'll divide by 2:

`y = 2x-4`

Finding the `x` intercept
On the `x` axis we know that the `y` value is alwways 0 so we can substitute this into the equation and rearrange to find an `x` value.

`0=4x-8`

Add 8 to both sides:

`8=4x`

Divide by 4:

`x=2`

So we know the `x` intercept is at the point `(2,0)`

Finding the `y` intercept

At the `y` intercept we know that the `x` value is always 0.

Finding the `y` value is easy. The `c` value in `y=mx+c` gives the `y` coordinate for the `y` intercept and we've already rearrange into that form we now know that the `y` value is -4!

So the `y` intercept is at the point `(0,-4)`

Answer 2

x-intercept: `2`
y-intercept: `-4`

Explanation:

Given: `4x-2y=8`

x-intercept
The x-intercept is the value of `x` when `y=0`
`color(white)("XXX")4x-2(0)=8 rArr x=2`

y-intercept
The y-intercept is the value of `y` when `x=0`
`color(white)("XXX")4(0)-2y=8 rArr y=-4`