L3 · Graphing a Sequence: Points on a Straight Line (First Quadrant)

Learning goal

“I can turn a table of values into ordered pairs (position, term), plot them on a first-quadrant coordinate grid, describe the graph of an arithmetic sequence as points on a straight line, and read terms - including future terms - from the graph.”

Ordered pair — the two numbers that name one point, written (position, term): position FIRST (distance from the vertical axis), term SECOND (distance from the horizontal axis).

Plot — to place a point on the grid at its ordered pair: move across by the first number, then up by the second.

Straight line — the points of an arithmetic sequence, if connected in order, lie on one straight line - never a curve, never scattered. This is the graph's signature.

Worked example

Graph the sequence 2, 4, 6, 8. Step 1: Table - Position: 1, 2, 3, 4 - Term: 2, 4, 6, 8. Step 2: Each row becomes ONE ordered pair, (position, term): (1, 2), (2, 4), (3, 6), (4, 8). Step 3: Plot them on a first-quadrant grid: across by the position, up by the term. Step 4: Look at the four points: they climb evenly and fit exactly on a straight line. That is not a coincidence - the constant difference (+2 each step) makes the points rise by the same amount for each step across, and equal rises make a straight line. The graph of an arithmetic sequence is a straight line of points. Say it plainly: position -> across, term -> up, and the constant difference is the steady climb that straightens the line.

Check yourself — explain it

The ordered pair for position 3, term 6 is written...

Paired problem — example still visible

Sequence 5, 10, 15: ordered pairs for positions 1-3 -> (1, 5), (2, 10), (3, 15)

Faded completion — last step is yours

"Sequence 3, 6, 9, 12: pairs are (1, 3), (2, 6), (3, ___), (4, 12)" -> (3, 9)

Ready to practise?

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

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