Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.6 Solutions: Introduction to Linear Polynomials

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.6 Solutions cover graph-based questions from Introduction to Linear Polynomials. This exercise helps students draw graphs of linear equations and understand the role of a and b in equations of the form y = ax + b.

In this exercise, students draw and study lines such as y = 4x, y = −6x, y = 3x − 1 and y = −2x − 3. The main learning is to observe how a and b work in y = ax + b. The value of a controls the slope or steepness of the line, while b tells where the line cuts the y-axis. Through these Class 9 Maths Chapter 2 Exercise 2.6 Solutions, students also understand why lines with the same slope are parallel and how positive and negative slopes change the direction of a graph.

Key Takeaways

Graph of a Line: A linear equation gives a straight-line graph.
Slope: The value of a in y = ax + b controls steepness and direction.
Y-intercept: The value of b shows where the line cuts the y-axis.
Parallel Lines: Lines with the same slope and different intercepts are parallel.

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.6 Solutions Structure 2026

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.6 Solutions

Ganita Manjari Class 9 Chapter 2 Exercise 2.6 belongs to the section on visualising linear relationships. It builds on earlier ideas of linear patterns and y = ax + b Class 9 by showing how equations appear on the coordinate plane. Students practise choosing points, plotting straight lines, comparing slopes, identifying y-intercepts and recognising parallel lines.

Here:

• a is the slope of the line.
• b is the y-intercept.
• If a > 0, the line slopes upward.
• If a < 0, the line slopes downward.
• Lines with the same slope and different y-intercepts are parallel.

These Class 9 Maths graph of linear equation answers help students understand how graphs of linear equations behave.

Exercise 2.6 Question 1

Draw the graphs of the following sets of lines. In each case, reflect on the role of ‘a’ and ‘b’.

(i) y = 4x, y = 2x, y = x

Solution:

All three equations are of the form:

y = ax + b

Here, b = 0 for all three lines. So, all lines pass through the origin (0, 0).

Points for drawing the graphs

Observation

The line y = 4x is the steepest because it has the greatest slope. The line y = x is the least steep among the three.

Answer: All three lines pass through the origin. As a increases from 1 to 4, the line becomes steeper.

(ii) y = −6x, y = −3x, y = −x

Solution:

All three equations are of the form:

y = ax + b

Here, b = 0, so all lines pass through the origin.

Points for drawing the graphs

Observation

Since the slopes are negative, all three lines slope downward from left to right. The line y = −6x is the steepest because its slope has the greatest magnitude.

Answer: All three lines pass through the origin and slope downward. As the magnitude of a increases, the line becomes steeper.

(iii) y = 5x, y = −5x

Solution:

Both equations have b = 0, so both lines pass through the origin.

Points for drawing the graphs

Observation

The lines have slopes of equal magnitude but opposite signs. So, y = 5x slopes upward and y = −5x slopes downward. They are mirror images of each other in the x-axis.

Answer: Both lines pass through the origin. y = 5x shows positive slope, while y = −5x shows negative slope.

(iv) y = 3x − 1, y = 3x, y = 3x + 1

Solution:

All three equations have the same slope:

a = 3

But their y-intercepts are different:

• For y = 3x − 1, b = −1
• For y = 3x, b = 0
• For y = 3x + 1, b = 1

Points for drawing the graphs

Observation

All three lines have the same slope, so they are parallel. The value of b shifts the line up or down.

Answer: The three lines are parallel because their slope is the same. Changing b shifts the line without changing its steepness.

(v) y = −2x − 3, y = −2x, y = 2x + 3

Solution:

The equations are:

• y = −2x − 3
• y = −2x
• y = 2x + 3

Points for drawing the graphs

Observation

The lines y = −2x − 3 and y = −2x have the same slope −2, so they are parallel. Their y-intercepts are different, so they cut the y-axis at different points.

The line y = 2x + 3 has positive slope, so it rises from left to right and is not parallel to the first two lines.

Answer: y = −2x − 3 and y = −2x are parallel. y = 2x + 3 has positive slope and is not parallel to them.

Final Answers for Exercise 2.6

Concept Used in Introduction to Linear Polynomials Exercise 2.6

Introduction to Linear Polynomials Exercise 2.6 focuses on the graph of a linear equation. A linear equation in the form y = ax + b gives a straight line.

Important points:

• a represents the slope of the line.
• b represents the y-intercept.
• If b = 0, the line passes through the origin.
• If a > 0, the line rises from left to right.
• If a < 0, the line falls from left to right.
• A larger absolute value of a makes the line steeper.
• Lines with the same slope and different y-intercepts are parallel.

These ideas are central to slope and y-intercept Class 9 and help students understand linear equation graph Class 9 questions.

About Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.6

Ganita Manjari Class 9 Chapter 2 Exercise 2.6 appears in the section “Visualising Linear Relationships”. It comes after students learn linear patterns, linear growth, linear decay and equations of the form y = ax + b.

These Class 9 Maths Chapter 2 Exercise 2.6 Solutions prepare students for:

• drawing graphs of linear equations,
• identifying slope,
• identifying y-intercept,
• comparing steepness,
• recognising parallel lines,
• and understanding graph-based linear polynomial Class 9 questions.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2