NCERT Solutions for Class 9th Maths Chapter 2 In-text Questions — Visualising linear relationships (Fig. 2.9)
Book page 31 Updated on2026-09-08
Q1.
Fig. 2.9 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 happens when a > 1 and when a < 1? (Hint: You may also plot the equations y = 3x and y = ⅓x on the same axes.)
Answer
Three conclusions, all visible at once when the lines share axes.
Every line y = ax passes through the origin (0, 0), whatever a is.
All of them rise from left to right, since a > 0.
The bigger a is, the steeper the line. Taking y = x as the reference: if a > 1 the line is steeper than y = x; if a < 1 it is less steep.
y = 3x, y = x and y = x/3 on one pair of axes. All three meet at the origin; only the steepness changes with a.
Why each conclusion must hold: • Put x = 0 in y = ax and you get y = 0 for every a. So (0, 0) is on all of them — there is no constant term to lift the line off the origin.
• Increase x by 1 and y increases by a. So a is literally the rise per unit of run, i.e. the slope. A larger rise over the same run is a steeper line.
• At x = 4, y = 3x is already at 12 while y = ⅓x has only reached 1⅓. The line y = x, with slope 1, makes equal angles with the two axes, so it is the natural dividing case between the two behaviours.
Try This: plot y = 3x and y = ⅓x on the same axes as the hint suggests. They are mirror images of each other in the line y = x — swapping x and y turns one equation into the other.