2x+3y=4

This is not slope btw 

When x=-4:
2(-4)+3y=4
3y=4+8
3y=12
y=4
So the ordered pair is (-4,4), I think

Okay, so we have 2x+3y=4. let's put this in slope intercept form.

We do that by subtracting 2x over and we now have 3y=-2x+4

Now we divide both sides by 3 and end up with y=(-2/3)x+4/3

Now let's plug in -4 for x.

y=(-2/3)(-4)+4/3  is y=8/3+4/3

8/3+4/3 =4

so y=4

Therefore, you coordinate pair is (-4,4) because when x is -4, y is 4. :D