Question

How do you find the x and y intercepts for `-3x+4y=8`?

Answer 1

Substitute in `0` for `x` or `y` to find that there is
an `x`-intercept at `(-8/3, 0)` and
a `y`-intercept at `(0, 2)`

Explanation:

An `x`-intercept of a graph occurs when the graph meets the `x`-axis, that is, at a point where `y = 0`. Similarly, a `y`-intercept occurs where `x = 0`.

To find the `x` and `y` intercepts, then, we simply substitute in `0` for `y` and `x` respectively.

Substituting `0` for `y` gives us

`-3x + 4(0) = 8`

`=> -3x = 8`

`=> x = -8/3`

Thus the `x`-intercept occurs at `(-8/3, 0)`.

Substituting `0` for `x` gives us

`-3(0) + 4y = 8`

`=> 4y = 8`

`=> y = 2`

So the `y`-intercept occurs at `(0, 2)`