NCERT Solutions for Class 9th Maths Chapter 2 In-text Questions — Visualising linear relationships (Fig. 2.11)
Book page 33 Updated on2026-09-08
Q1.
Fig. 2.11 shows all the three graphs on the same axes. Does this help you to conclude anything about the linear equation y = – ax, a > 0, as a varies? What will happen when a > 1 and when a < 1?
Answer
The picture mirrors the previous one, with one crucial change of sign.
Every line y = −ax still passes through the origin.
All of them now fall from left to right, because the slope −a is negative — these are pictures of linear decay.
Steepness is decided by the size of a, not its sign: if a > 1 the line falls more steeply than y = −x; if a < 1 it falls more gently.
y = −3x, y = −x and y = −x/3. Compare with the previous figure: each line is its positive-slope partner reflected in the x-axis.
Why the whole family is just a reflection: replacing a by −a replaces every output y by −y and leaves x untouched. Geometrically that is a reflection in the x-axis, which cannot change how steep a line is — only which way it leans. So the pair y = 3x and y = −3x make equal angles with the x-axis on opposite sides. Increasing x by 1 now decreases y by a, so a bigger a means a faster fall.
Tip: the useful summary is: the sign of the slope tells you growth or decay; the size of the slope tells you how fast.