An ordered pair is an instruction in two parts. The word ordered is doing real work, because swapping the parts sends you somewhere else.
A single number fixes a position on a line. Two numbers fix a position on a flat surface. The coordinate plane is just two number lines crossed at their zeros, which is why everything you learned about signs in Skill 0.01 still applies here.
Each point gets exactly one name, written (x, y). The first number is a horizontal instruction and the second is a vertical one, and that assignment never changes.
The horizontal line is the x-axis and the vertical line is the y-axis. They cross at the origin, the point (0, 0). The two axes cut the plane into four quadrants, numbered counterclockwise starting from the upper right.
Start every plot at the origin. The first number moves you horizontally, right for positive and left for negative. The second moves you vertically.
The first number is always horizontal and the second is always vertical. Start at the origin, make the x move, then the y move.
Because both numbers look alike on the page, it is easy to plot the second one first. That lands you somewhere else entirely. (3, 4) and (4, 3) are two distinct locations.
Both points use the digits 3 and 4, yet they sit one square apart in each direction.
Sense check: say the pair aloud as "across 3, up 4" before your pencil touches the grid.
The second half of the trap is counting from the wrong line. The x-coordinate is a horizontal distance measured from the y-axis, and the y-coordinate is a vertical distance measured from the x-axis. Reading a plotted point means running a straight line to each axis and reading the number there.
Once you know the signs of a pair, you know its quadrant before plotting anything. That makes the quadrant a fast check on your own work.
Plot (−4, 3) and name its quadrant.
Start at the origin. The x-coordinate is −4, so move 4 left. The y-coordinate is 3, so move 3 up from there.
The point sits in Quadrant II. Sense check: the signs are negative then positive, which the table names as Quadrant II.
A point sits 2 units right of the y-axis and 5 units below the x-axis. Name it.
Distance from the y-axis is the x-coordinate, and right is positive, so x = 2. Distance from the x-axis is the y-coordinate, and below is negative, so y = −5.
The point is (2, −5), in Quadrant IV. Sense check: right and down is the pattern for Quadrant IV.
A campus map puts the origin at the flagpole, with east positive and north positive. The gym is at (5, −2). Describe where it stands.
The first number is horizontal: 5 units east. The second is vertical: −2 means 2 units south.
The gym is 5 east and 2 south of the flagpole, in Quadrant IV. Sense check: reading it as (−2, 5) would place the gym west and north instead, on the far side of campus.
Skill 0.08 returns to a single unknown and asks you to solve for it rather than substitute into it. The trap there is reaching for the same operation the equation shows instead of its inverse, so an equation built by adding gets solved by adding again.