Topic 9 of 9

Plotting points on the coordinate plane

Step 7 · Fraction and decimal arithmetic topics

Use two number lines at right angles to name any point with an ordered pair, plot points, and graph number patterns to see how they grow.

The axes and the origin

A coordinate plane is made of two number lines that cross at right angles. The line across is the x-axis; the line going up is the y-axis. They meet at 0 on both, a point called the origin.

The x-axis runs across and the y-axis runs up. They meet at the origin, (0, 0).

Plotting a point

A point is named by an ordered pair (x, y). Start at the origin, go x across, then y up. The order matters: (2, 5) and (5, 2) are different points.

(2, 5) is 2 across and 5 up; (5, 2) is 5 across and 2 up.

Example: Plotting a point

Plot (4, 3).

Start at the origin.
Go 4 across along the x-axis.
Go 3 up.

AnswerThe point 4 across and 3 up

Patterns on the plane

Points can show a pattern. The rule "y is 2 more than x" gives the pairs (0, 2), (1, 3), (2, 4), (3, 5). Plotted, they make a straight line.

Points where y is 2 more than x: (0, 2), (1, 3), (2, 4), (3, 5) and (4, 6) lie on a straight line.

Example: Two patterns

Pattern A starts at 0 and adds 3. Pattern B starts at 0 and adds 6. Write the first four pairs (A, B).

A: 0, 3, 6, 9.
B: 0, 6, 12, 18.
Pairs: (0, 0), (3, 6), (6, 12), (9, 18).

AnswerEach B number is twice the A number.

Distance along a grid line is easy to find: from (2, 3) to (7, 3) is 7 − 2 = 5 units across.

Try it yourself

Work each one on paper first, then open the answer to check.

What are the coordinates of the origin?
Show answer
(0, 0).
Which point is 6 across and 1 up?
Show answer
(6, 1).
Is (3, 7) the same point as (7, 3)?
Show answer
No. (3, 7) is 3 across and 7 up; (7, 3) is 7 across and 3 up.
How far is it from (1, 4) to (1, 9)?
Show answer
5 units, straight up.
The rule is "y is 3 times x". What is y when x is 4?
Show answer
12. The point is (4, 12).