Question

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

Answer 1

x-intercept: `4`
y-intercept: `-8`

Explanation:

The x-intercept is the value of `x` where the equation crosses the X-axis; that is it is the value of `x` when `y=0`.
Substituting `0` for `y` in `2x-y=8`
`color(white)("XXX")2x-0=8color(white)("xxx")rarrcolor(white)("xxx")x=4`
[Some instructors prefer to have the intercept written as as a coordinate pair; in this case, the coordinates for the x-intercept would be `(4,0)`].

Similary, the y-intercept is the value of `y` when `x=0`.
Substituting `0` for `x` in `2x-y=8`
`color(white)("XXX")2 * 0 -y =8 color(white)("xxx")rarrcolor(white)("xxx")y=-8`
[...or, given as a coordinate pair: `(0,-8)`].

Answer 2

See the entire solution process below:

Explanation:

To find the `y` intercept, set `x` equal to `0` and solve for `y`:

`2x - y = 8` becomes:

`(2 * 0) - y = 8`

`0 - y = 8`

`-y = 8`

`color(red)(-1) * -y = color(red)(-1) * 8`

`y = -8`

The y-intercept is `-8` or `(0, -8)`

To find the `x` intercept, set `y` equal to `0` and solve for `x`:

`2x - y = 8` becomes:

`2x - 0 = 8`

`2x = 8`

`(2x)/color(red)(2) = 8/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 4`

`x = 4`

The x-intercept is `4` or `(4, 0)`