NCERT Class 9 Maths Exercise 2.6 Solutions – Visualizing Linear Relationships

Short Intro

Exercise 2.6 introduces students to the graphical representation of linear equations. In this exercise, students learn how to draw straight-line graphs, identify slopes, compare parallel lines, and understand the role of coefficients in equations of the form (y=ax+b). These step-by-step solutions simplify graph plotting and linear relationship concepts for Class 9 learners.

Quick Information Box

Topic Details
Chapter Introduction to Linear Polynomials
Exercise Exercise 2.6
Subject Mathematics
Class Grade 9
Main Concepts Graphs of Linear Equations
Difficulty Level Moderate
Useful For School Exams & Foundation Maths

Concepts Used (Topics Covered)

  • Linear Relationships
  • Straight Line Graphs
  • Coordinate Geometry
  • Slope of a Line
  • y-Intercept
  • Parallel Lines
  • Positive and Negative Slopes
  • Graph Plotting

Important Formulas

General Linear Equation

Equation Passing Through Origin

Positive Slope

Negative Slope

Questions & Step-by-Step Solutions

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

(ii) y = – 6x, y = – 3x, y = – x

(iii) y = 5x, y = –5x

(iv) y = 3x – 1, y = 3x, y = 3x + 1

(v) y = –2x – 3, y = –2x, y = 2x + 3

Final Understanding

Role of (a)

  • Determines slope or steepness.
  • Positive (a) → upward line.
  • Negative (a) → downward line.

Role of (b)

  • Determines y-intercept.
  • Changes vertical position of graph.
  • Same slope but different (b) gives parallel lines.

Common Mistakes

❌ Plotting incorrect coordinates
❌ Confusing slope with y-intercept
❌ Using wrong sign for negative slopes
❌ Joining points inaccurately

Exam Tips

✔ Always make coordinate table first
✔ Plot at least two correct points
✔ Use ruler for straight lines
✔ Remember: same slope ⇒ parallel lines

Practice MCQs

1. Which equation passes through origin?

A) (y=2x+1)
B) (y=3x)
C) (y=x-5)
D) (y=4x+2)

Answer

✅ B) (y=3x)

2. Which line has negative slope?

A) (y=5x)
B) (y=2x+1)
C) (y=-3x)
D) (y=x)

Answer

✅ C) (y=-3x)

3. Parallel lines have:

A) Same intercept
B) Same slope
C) Same equation
D) Same coordinates

Answer

✅ B) Same slope

4. In y=ax+b, b represents:

A) slope
B) coefficient
C) y-intercept
D) x-coordinate

Answer

✅ C) y-intercept

FAQ Section

Q1. What is a linear graph?

A straight-line graph representing a linear equation is called a linear graph.

Q2. What is slope?

Slope measures the steepness of a line.

Q3. What is y-intercept?

It is the point where the graph cuts the y-axis.

Q4. When are two lines parallel?

Two lines are parallel when their slopes are equal.

Q5. Why do some graphs pass through origin?

Graphs pass through origin when y-intercept is zero.

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