A point is written (x, y). The x coordinate says how far across from the origin, the y coordinate how far up. Left of the y-axis x is negative; below the x-axis y is negative.

P is (−3, 2): 3 left and 2 up. Q is (4, −1): 4 right and 1 down. Swapping the numbers gives a different point: (2, −3) is somewhere else entirely.

The midpoint of a line segment is halfway along it. Its coordinates are the means of the end points' coordinates.

1. A(−2, 5) and B(6, 2)
2. x: (−2 + 6) ÷ 2 = 4 ÷ 2 = 2
3. y: (5 + 2) ÷ 2 = 7 ÷ 2 = 3.5
4. midpoint (2, 3.5)

To find an end point from the midpoint, take the step from A to M and do it again. A(1, 3) and M(4, 1): the step is +3 across and −2 up, so B is (7, −1). The slip to avoid: finding the midpoint of A and M instead.

For y = 2x − 1, substitute each x, with negatives in brackets: x = −2 gives y = 2 × (−2) − 1 = −5. Plot every pair; for y = mx + c they always line up, so join them with a ruler. If one point is off the line, recheck that value rather than bending the line.

Two lines have no x term or no y term. x = 3 is the vertical line where every point has x coordinate 3. y = 3 is horizontal. The x-axis itself is y = 0.