Given a table of (x, y) values, find the rule. It's pattern-spotting raised to algebra.
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y = m·x + b
From a table to a rule
- Look at how y changes when x goes up by 1 — that constant jump is the slope m.
- Find y when x = 0 — that's the y-intercept b.
- Write y = mx + b, then check it against every row of the table.
- Plot the points: with the right m and b they all land on the line above.
Your turn
A table shows (0, 3), (1, 5), (2, 7), (3, 9). What's the equation?
Watch out
If the differences aren't constant, it isn't a line. Check the differences of the differences — if those are constant, it's a quadratic y = ax² + bx + c, not y = mx + b.
Try it
x: 1, 2, 3, 4 → y: 3, 5, 7, 9. Rule?
y goes up by 2 each step. y = 2x + 1. Check: x=4 → 2(4)+1 = 9. ✓
If y goes up by a constant, it's linear: y = mx + b. If the difference of differences is constant, it's quadratic: y = ax² + bx + c.