NCERT Solutions for Class 9th Maths Chapter 2 Introduction to Linear Polynomials
Updated on 2026-09-19
About this chapter
An algebraic expression is built from numbers, variables and operation signs. In 4 x + 5 y + 3 the parts 4 x , 5 y and 3 are the terms , x and y are the variables , 4 and 5 are the coefficients and 3 is the constant . A univariate polynomial (one-variable polynomial) uses a single variable and its powers. The highest power present is its degree : 5 y ³ + y ² + 2 y − 1 is cubic (degree 3), x ² + 5 x + 1 is quadratic (degree 2), 3 z + 7 is linear (degree 1), and a non-zero constant such as 8 = 8 x ⁰ has degree 0. A polynomial is an input–output machine: put a value of the variable in, get a number out. For 2 x + 3, an input of 4 gives 11 and an input of −6 gives −9. This is what is meant by calling 2 x + 3 a function of x . The defining behaviour of a linear polynomial: equal steps in the va
- Introduction
- Introduction (Example 3)
- Linear Polynomials (Example 4)
- Linear Polynomials (Example 5)
- Linear Polynomials
- Exploring linear patterns
- Exploring linear patterns (Example 7)
- Exploring linear patterns (Example 8)
- Linear growth and linear decay (Example 9)
- Linear growth and linear decay (Example 10)
Quick revision
| Idea | What it means | Symbolic form | Example from the chapter |
|---|---|---|---|
| Term / coefficient / constant | The pieces added together; the number multiplying a variable; the number-only term | 4x + 5y + 3 | terms 4x, 5y, 3; coefficients 4, 5; constant 3 |
| Univariate polynomial | One variable and its whole-number powers only | anxn + … + a1x + a0 | 5y³ + y² + 2y − 1 |
| Degree | The highest power of the variable that appears | deg | deg(2x² − 5x + 3) = 2 |
| Linear polynomial | Degree exactly 1 | ax + b, a ≠ 0 | 3z + 7, 200 + 50m, 2n − 1 |
| Constant polynomial | Degree 0 — the value never changes | c = cx⁰ | 8 |
| Linear equation | A linear polynomial set equal to a constant | ax + b = c | 2x + 10 = 64 gives x = 27 |
| Value of a polynomial | Substitute the number for the variable | p(k) | 2x + 3 at x = 4 is 11 |
| Linear pattern | Consecutive terms differ by a fixed amount | tn = an + b | 1, 3, 5, 7, … from 2n − 1 |
| Linear growth | A fixed amount is added each equal interval | y = ax + b, a > 0 | C(d) = 100 + 60d |
| Linear decay | A fixed amount is subtracted each equal interval | y = ax + b, a < 0 | h(t) = 3 − 0.5t |
| Slope | The change in y for a 1-unit change in x | a in y = ax + b | slope of y = 2x − 1 is 2 |
| y-intercept | Signed distance from O at which the line cuts the y-axis | b; point (0, b) | y = 3x − 2 cuts the y-axis at (0, −2) |
| Parallel lines | Same slope, different y-intercepts | y = ax + b₁, y = ax + b₂ | y = 2x − 1, y = 2x + 1, y = 2x + 5 |
Exercises
- Think and Reflect — Introduction Page 17
- In-text Questions — Introduction (Example 3) Page 17
- Think and Reflect — Introduction (Example 3) Page 17
- Exercise Set 2.1 — Introduction Page 18–19
- Think and Reflect — Linear Polynomials (Example 4) Page 19
- Think and Reflect — Linear Polynomials (Example 5) Page 19
- Think and Reflect — Linear Polynomials Page 20
- Exercise Set 2.2 — Linear Polynomials Page 21
- Think and Reflect — Exploring linear patterns Page 22
- Think and Reflect — Exploring linear patterns Page 22
- Think and Reflect — Exploring linear patterns (Example 7) Page 23
- Think and Reflect — Exploring linear patterns (Example 8) Page 23
- Exercise Set 2.3 — Exploring linear patterns Page 23–24
- Think and Reflect — Linear growth and linear decay (Example 9) Page 24
- Think and Reflect — Linear growth and linear decay (Example 10) Page 25
- Exercise Set 2.4 — Linear growth and linear decay Page 25–26
- Think and Reflect — Linear Relationships (Example 11) Page 27
- Exercise Set 2.5 — Linear Relationships Page 27
- Think and Reflect — Visualising linear relationships Page 28
- In-text Questions — Visualising linear relationships (Examples 13, 14) Page 29
- In-text Questions — Visualising linear relationships (Fig. 2.9) Page 31
- In-text Questions — Visualising linear relationships (Fig. 2.11) Page 33
- Think and Reflect — Visualising linear relationships Page 33
- Think and Reflect — Visualising linear relationships (Fig. 2.13) Page 35
- Exercise Set 2.6 — Visualising linear relationships Page 36
- Chapter 2 Introduction to Linear Polynomials — End-of-Chapter Exercises Page 36–39