NCERT Solutions for Class 9th Maths Chapter 2 In-text Questions — Visualising linear relationships (Examples 13, 14)
Book page 29 Updated on2026-09-19
Q1.
Let us plot the points (– 3, 6), (– 2, 4), (0, 0), (1, – 2), (2, – 4), (3, – 6) in the coordinate plane on a graph paper as shown in Fig. 2.7. Join the points (– 3, 6) and (3, – 6) using a ruler. Doing so, observe that all five points lie on a straight line. Can you guess the equation of this line by looking at the relationship between the x and y coordinates of each point?
Fig. 2.7, page 29 — the six points plotted on graph paper.
Answer
In every listed point the y-coordinate is −2 times the x-coordinate.
x
−3
−2
0
1
2
3
y
6
4
0
−2
−4
−6
y ÷ x
−2
−2
—
−2
−2
−2
Equation of the line: y = −2x
Why this is the right form: the ratio y/x is the same for every point, so y is a constant multiple of x — that constant is the slope, here −2. Because there is no constant term, the point (0, 0) satisfies the equation, and indeed the line passes through the origin. The negative slope shows itself in the picture: as x moves right, y comes down, so the line falls from upper left to lower right.
Check it yourself: substitute the point that was not used to draw the line, say (−2, 4): −2(−2) = 4. ✓ A single failed check would mean the guessed equation is wrong.
Q2.
Draw the graphs of y = ½x, y = x, y = 2x by selecting suitable points on these lines. (Hint: In order to graph y = ½x, we could take the points (0, 0) and (4, 2). Can you verify that these lie on the line?)
Answer
Verifying the hint’s two points on y = ½x:
(0, 0): ½ × 0 = 0 ✓
(4, 2): ½ × 4 = 2 ✓
Both satisfy the equation, so both lie on the line — and two points are all a straight line needs.
Convenient points for the three lines:
Line
Point 1
Point 2
Slope
y = ½x
(0, 0)
(4, 2)
½
y = x
(0, 0)
(4, 4)
1
y = 2x
(0, 0)
(4, 8)
2
Why choose x = 0 and x = 4:x = 0 always gives the y-intercept for free, and a multiple of the denominator (here 4, a multiple of 2) keeps the second coordinate a whole number so it can be plotted exactly on the grid. Picking x = 3 for y = ½x would force you to plot 1.5 by eye. Also, taking the two points far apart makes the ruled line more accurate — a small slip in plotting two nearby points tilts the whole line.
Tip: All three lines pass through the origin because each has the form y = ax with no constant term. Their difference is only how steeply they climb.