NCERT Solutions for Class 9th Maths Chapter 2 Think and Reflect — Visualising linear relationships
Book page 33 Updated on2026-09-08
Q1.
Differentiate between the graphs of the equations y = 3x + 1, and y = –3x + 1.
Answer
y = 3x + 1
y = −3x + 1
Slope
+3
−3
y-intercept
1, at (0, 1)
1, at (0, 1)
Direction
rises to the right (growth)
falls to the right (decay)
Cuts the x-axis at
(−⅓, 0)
(⅓, 0)
Steepness
the same — both change y by 3 for a 1-unit change in x
Both lines cross the y-axis at (0, 1), but with opposite slopes; they are mirror images of each other in the y-axis.
Why they meet exactly once, and where: equate them.
3x + 1 = −3x + 1
6x = 0 x = 0, so y = 1
Their only common point is (0, 1) — the shared y-intercept. The x-intercepts come from 3x + 1 = 0 and −3x + 1 = 0, giving x = −⅓ and x = ⅓: equal distances from the origin on opposite sides, which is the reflection in the y-axis showing up in the numbers. Replacing x by −x turns one equation into the other, and that substitution is reflection in the y-axis.
Check it yourself: at x = 2 the two lines give 7 and −5. They are 12 units apart, and that gap grows by 6 for every extra unit of x — the difference of the two slopes.