Two number lines crossed at right angles turn every pair of numbers into a place. That is the whole invention. Slide a point around and watch it walk, tap the four quadrants to see why their signs are what they are, then step through finding where a graph crosses each axis.
The coordinate plane
The sign map
Why counterclockwise? Quadrant I is the corner where both coordinates are positive — the corner you meet first walking right and up. From there the numbering turns counterclockwise, so each step flips exactly one sign at a time.
The two questions
An intercept is a point where a graph meets an axis — and on an axis, one of the two coordinates is forced to 0. Substituting that zero is not a trick to memorise; it is just writing down where you already are.
(3, 2)Quadrant I
First coordinate — x — run3
−6 left06 right
Second coordinate — y — rise2
−6 down06 up
Or jump to a point worth seeing
The order is not negotiable. An ordered pair is written (x, y): the first number is the horizontal move, the second is the vertical one. Alphabetical order — x before y — is the only reminder you need. Coordinates do not have to be whole numbers; (1.5, −2.75) is a perfectly ordinary point.
The recipe, both directions. For the y-intercept, set x = 0 and solve for y. For the x-intercept, set y = 0 and solve for x. The zero always goes in for the other letter — the crossed wires there are what cost most people the marks.
The trap. A point sitting on an axis is in no quadrant at all. The quadrants are the four open blocks; the axes are the fences between them, and a fence belongs to neither field. So (0, −4) is not in Quadrant IV — it is on the y-axis. Likewise (−5, 0) is on the x-axis, not in Quadrant III.
The trap. An intercept is a point, so it has two coordinates. The x-intercept (6, 0) puts the nonzero number first; the y-intercept (0, 4) puts it second. You will also see intercepts reported as bare numbers — “the x-intercept is 6” — and both conventions are standard. Just never write the pair backwards.