Grade 6 › U09 Patterns & Functions

Grade 6 › U09 Patterns & Functions › L3
NUMBER · GRADE 6 · ALBERTAOUTCOME AB-MAT6-P1

L3 · Functions on the Cartesian plane

Learning goal

“I can turn each row of a table of values into an ordered pair, plot it on the Cartesian plane - independent variable across, dependent variable up - and read values back off a graph in both directions.”

Cartesian plane — a grid with two axes where each point shows a pair of values that belong together.
Horizontal axis — the axis running left to right. The independent variable (input) always goes here.
Vertical axis — the axis running up and down. The dependent variable (output) always goes here.
Ordered pair — a pair of numbers written (input, output), like (3, 36): go across to the input first, then up to the output. The order matters.
Worked example

A cyclist rides 12 km every hour. Table: hours 0 -> 0 km, 1 -> 12 km, 2 -> 24 km, 3 -> 36 km. Step 1: Turn each row into an ordered pair (hours, kilometres): (0, 0), (1, 12), (2, 24), (3, 36). Step 2: Plot (2, 24): start at 0, move across to 2 on the horizontal axis (hours - the independent variable), then move up to 24 on the vertical axis (kilometres - the dependent variable). Mark the point where across-2 meets up-24. Step 3: Plot the rest the same way. The four points climb in a straight line: each extra hour adds the same 12 km, so the points rise evenly.

Check yourself — explain it

In the ordered pair (2, 24) for this cyclist, the 2 is...

Paired problem — example still visible

Write the ordered pair for the row "3 hours -> 36 km". -> (3, 36)

Faded completion — last step is yours

"A pay graph has hours on the horizontal axis. The point for 5 hours and $75 is (5, ___)." -> 75

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz