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:
$3y + 4x = 8$
$3(0) + 4x = 8$
$4x = 8$
$x = \frac{8}{4}$
$x=2$
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.