Plotting points in the first quadrant

Every point on a coordinate plane has an address called an ordered pair. It is written as (x, y), and the order really matters, just like the words in an address.

The first number, x, tells you how far to move across. Start at zero, where the two axes cross, and count spaces to the right. The second number, y, tells you how far to move up from there.

Try it with (3, 4). Start at zero. Move 3 spaces right along the bottom axis. Now move 4 spaces straight up. Mark that spot. You just plotted (3, 4)!

You can also work backwards. If a point is already on the grid, count how far across it is, then how far up. Write the across number first and the up number second, and you have its ordered pair.

A handy trick: x comes before y in the alphabet, and across comes before up. Say it a few times and you will never mix them up again.

A coordinate plane is a flat grid made by two number lines that cross at zero. The horizontal one is called the x-axis, and the vertical one is called the y-axis. The spot where they cross is called the origin, and its ordered pair is (0, 0).

These two axes split the plane into four parts called quadrants. In this lesson we stay in the first quadrant, the part up and to the right of zero, where both numbers of every ordered pair are positive.

To plot a point, you use its ordered pair (x, y). Think of the two numbers as moves. The x number says how far to move right from the origin. The y number says how far to move up from there. For example, to plot (2, 5), go 2 right, then 5 up, and make your mark.

Plotting points lets you turn real information into a picture. If you track how far you bike each hour, you can plot hours as x and distance as y, and the points will show your trip at a glance.

Here are the big ideas to remember about the coordinate plane.

First, we locate points using ordered pairs. An ordered pair (x, y) describes a point by its distance from the two axes: x is the distance across from the y-axis, and y is the distance up from the x-axis.

Second, every ordered pair matches exactly one point on the plane, and every point matches exactly one ordered pair. They are like names and the people they belong to.

Third, you can graph information by making a table of pairs and plotting each one. If you know that 1 hour of practice means 10 baskets scored and 2 hours means 20 baskets, the points (1, 10) and (2, 20) turn those facts into a picture you can read.