Which comes first in a coordinate, x or y?

x always comes first. (4, 1) means 4 across and 1 up.

Which quadrant is $(-3, 5)$ in?

Negative x and positive y put it in quadrant II, the top left.

The Coordinate Plane: Axes, Quadrants and Plotting Points

How two number lines make a map of the plane, how to read and plot coordinates, what the four quadrants are, and how a graph is simply every point that makes an equation true.

3 min read Supports 3 lessons

A number line gives every number a position along one direction. Put a second number line at right angles to the first, crossing at zero, and you can give every point on a flat surface an address. This idea, due to René Descartes, links algebra to pictures.

Four points, one in each quadrant.

Reading coordinates

The horizontal line is the $x$ -axis and the vertical one is the $y$ -axis. They cross at the origin, $(0, 0)$ . A point's coordinates $(x, y)$ are always written in the same order: across first, then up or down.

Key idea

Read $x$ first, then $y$ : along the corridor, then up the stairs.

Watch out

$(3, 2)$ and $(2, 3)$ are different points. The order matters, which is why they are called ordered pairs.

The four quadrants

The axes split the plane into four quadrants, numbered anticlockwise from the top right.

\text{I}: (+, +) \qquad \text{II}: (-, +) \qquad \text{III}: (-, -) \qquad \text{IV}: (+, -)

Points on an axis belong to no quadrant. Any point on the $x$ -axis has $y = 0$ , and any point on the $y$ -axis has $x = 0$ .

From points to graphs

An equation in $x$ and $y$ picks out the points whose coordinates make it true. Plot enough of them and a shape appears. That shape is the equation's graph.

$y = 2x - 1$
Which points satisfy this equation?

1/5

Key idea

A point lies on a graph exactly when its coordinates satisfy the equation. To test whether $(3, 5)$ is on $y = 2x - 1$ , substitute: $2(3) - 1 = 5$ ✓.

Tip

Once points have coordinates, distances, midpoints, slopes and even circles can all be calculated with algebra instead of a ruler.

Common questions

Which comes first in a coordinate, x or y?: $x$ always comes first. $(4, 1)$ means $4$ across and $1$ up.
Which quadrant is $(-3, 5)$ in?: Negative $x$ and positive $y$ put it in quadrant II, the top left.

Practise coordinate plane

The The Coordinate Plane lesson has worked examples and unlimited practice that adapts to you.

Open the lesson

Graphs & Functions

The Coordinate Plane: Axes, Quadrants and Plotting Points

How two number lines make a map of the plane, how to read and plot coordinates, what the four quadrants are, and how a graph is simply every point that makes an equation true.

3 min read Supports 3 lessons

Four points, one in each quadrant.

Reading coordinates

Key idea

Read $x$ first, then $y$ : along the corridor, then up the stairs.

Watch out

$(3, 2)$ and $(2, 3)$ are different points. The order matters, which is why they are called ordered pairs.

The four quadrants

The axes split the plane into four quadrants, numbered anticlockwise from the top right.

\text{I}: (+, +) \qquad \text{II}: (-, +) \qquad \text{III}: (-, -) \qquad \text{IV}: (+, -)

Points on an axis belong to no quadrant. Any point on the $x$ -axis has $y = 0$ , and any point on the $y$ -axis has $x = 0$ .

From points to graphs

An equation in $x$ and $y$ picks out the points whose coordinates make it true. Plot enough of them and a shape appears. That shape is the equation's graph.

$y = 2x - 1$
Which points satisfy this equation?

1/5

Key idea

A point lies on a graph exactly when its coordinates satisfy the equation. To test whether $(3, 5)$ is on $y = 2x - 1$ , substitute: $2(3) - 1 = 5$ ✓.

Tip

Once points have coordinates, distances, midpoints, slopes and even circles can all be calculated with algebra instead of a ruler.

Common questions

Which comes first in a coordinate, x or y?: $x$ always comes first. $(4, 1)$ means $4$ across and $1$ up.
Which quadrant is $(-3, 5)$ in?: Negative $x$ and positive $y$ put it in quadrant II, the top left.

Practise coordinate plane

The The Coordinate Plane lesson has worked examples and unlimited practice that adapts to you.

Open the lesson