NCERT Solutions for Class 9th Maths Chapter 2 Think and Reflect — Visualising linear relationships (Fig. 2.13)
Book page 35 Updated on2026-09-08
Q1.
Does this help you to conclude anything about the linear equation y = ax + b when a is fixed but b varies? (Hint: In these equations a = 2, and b takes the values –1, 1 and 5, respectively.)
Answer
Yes. With a = 2 fixed and b = −1, 1, 5 the three lines are parallel: same tilt, different heights.
Line
Slope a
y-intercept b
Cuts the y-axis at
y = 2x − 1
2
−1
(0, −1)
y = 2x + 1
2
1
(0, 1)
y = 2x + 5
2
5
(0, 5)
Changing b slides the line straight up or down; it never tilts, so the three lines never meet.
Why they can never meet: suppose 2x + b₁ = 2x + b₂ at some x. The 2x cancels and we are left with b₁ = b₂. So two lines with the same slope and different intercepts have no common point at all — they are parallel. Better still, at any given x the vertical gap between y = 2x + 5 and y = 2x + 1 is (2x + 5) − (2x + 1) = 4, the same everywhere. A constant gap is exactly what “parallel” means.
Tip: Adding b to a linear expression shifts its graph b units vertically — up if b is positive, down if negative. The slope, being the rate of change, is untouched by adding a constant.