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.
Fig. 2.5, page 28 — the straight line y = 2x + 1, with A (0, 1) and B (3, 7) marked on it.
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.