Q1.
Identify other points on the line by completing the following table. (x: 1, 2, 5, 7, 9, 12, 20; y: 3, …, …, 15, …, …, …)
Answer
The line is y = 2x + 1, so double each x and add 1.
| x | 1 | 2 | 5 | 7 | 9 | 12 | 20 |
|---|---|---|---|---|---|---|---|
| y = 2x + 1 | 3 | 5 | 11 | 15 | 19 | 25 | 41 |
So (1, 3), (2, 5), (5, 11), (7, 15), (9, 19), (12, 25) and (20, 41) all lie on the line.
Why substituting is a genuine test: a point lies on a line exactly when its coordinates satisfy the equation of that line — the equation is nothing but the membership rule for the set of points on the line. So (7, 15) belongs because 2(7) + 1 = 15 ✓, while (7, 14) does not, and no amount of careful drawing would change that. Checking by substitution is exact; reading off a graph is only approximate.
Tip: the two given entries let you find the rule even if you had forgotten it: from x = 1 to x = 7 the value climbs 15 − 3 = 12 over 6 steps, so 2 per step — the slope — and then 3 = 2(1) + 1 gives the intercept.