NCERT Solutions for Class 9th Maths Chapter 2 Think and Reflect — Visualising linear relationships

Book page 28 Updated on2026-09-19

Q1.
Identify other points on the line by completing the following table.
−2−112345−1123456780x-axisy-axisA (0, 1)B (3, 7)
Fig. 2.5, page 28 — the straight line y = 2x + 1, with A (0, 1) and B (3, 7) marked on it.
x125791220
y315
Answer

The line is y = 2x + 1, so double each x and add 1.

x125791220
y = 2x + 1351115192541

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.
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