Question

Which ordered pair represents the x-intercept for the linear equation, 3y + 4x = 8?

Answer 1

3y + 4x = 8 represents a line on the x-y plane, looking like the image I attached.

To find the x-intercept means to find the place where the line intersects the x-axis. If the line is intersecting the x-axis, then the point where it intersects the x-axis must be a place where y = 0. If y didn't equal 0, then that point wouldn't be on the x-axis.

So, to find the x-intercept, we set y in the given equation to 0, like this:

`3y + 4x = 8`

`3(0) + 4x = 8`

`4x = 8`

`x = (8)/(4)`

`x=2`
So,
`x=2`. We assumed that
`y=0` to find the x-intercept at the beginning. Then, our ordered pair in the usual order
`(x,y)` is
`(0,2)`. You can see this is correct by looking at the attached graph.