Question

How do you find the x and y intercept of `4x+8y=12`?

Answer 1

Y int at `(0,3/2)`
X int at `(3,0)`

Explanation:

The line is easier to visualize when the equation is in slope-intercept form:
`4x+8y=12`

Divide each side by 4:
`x+2y=3`
`2y=-x+3`
`y=-1/2x+3/2`

Y-intercept (plug in 0 for x):
`y=-1/2(0)+3/2`
`y=3/2`

X-intercept (plug in 0 for y):
`0=-1/2x+3/2`
`-3/2=-1/2x`
`x=3`

Answer 2

To find the `x` intercept substitute `0` for `y` in the equation.

To find the `y` intercept substitute `0` for `x` in the equation.

See the full explanation below

Explanation:

To find the `x` intercept substitute `0` for `y` in the equation and solve for `x`.

`4x + (8 xx 0) = 12`

`4x + 0 = 12`

`4x = 12`

`(4x)/color(red)(4) = 12/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 3`

`x = 3`

The x-intercept is `3` or (3, 0)

To find the `y` intercept substitute `0` for `x` in the equation and solve for `y`.

`(4 xx 0) + 8y = 12`

`0 + 8y = 12`

`8y = 12`

`(8y)/color(red)(8) = 12/color(red)(8)`

`(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = (4 xx 3)/(4 xx 2)`

`y = (cancel(4) xx 3)/(cancel(4) xx 2)`

`y = 3/2`

The y-intercept is `3/2` or (0, 3/2)