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NCERT Class 9 Mathematics Exercise Set 2.6 Solutions: Introduction to Linear Polynomials
AI-written, checked on 23 Oct 2026
Solutions written by Shishya, checked — not the board's official answers
Step-by-step working for every question of Exercise Set 2.6 in NCERT's Class 9 Mathematics book, chapter “Introduction to Linear Polynomials”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.
How these were checked: the solutions were drafted with AI and then read and corrected on 23 Oct 2026. Every numerical final answer is recomputed from the question's own numbers by a calculator check that runs before each release; proofs and explanations were read, not machine-checked. The NCERT textbook is the authority — if something here disagrees with it, follow the book.
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Ex 2.6 Q1
Draw each set of lines and say what a and b do: (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.
- For each line take two or three values of x, work out y, plot the points and join them with a ruler.
- (i) y = 4x: (0, 0), (1, 4); y = 2x: (0, 0), (1, 2); y = x: (0, 0), (1, 1). All three pass through the origin and rise to the right; the larger a is, the steeper the line.
- (ii) y = −6x: (0, 0), (1, −6); y = −3x: (0, 0), (1, −3); y = −x: (0, 0), (1, −1). All pass through the origin and fall to the right; the larger the size of a, the steeper the fall.
- (iii) y = 5x: (0, 0), (1, 5); y = −5x: (0, 0), (1, −5). Equally steep, one rising and one falling: each is the mirror image of the other in the y-axis. The sign of a decides rise or fall.
- (iv) y = 3x − 1: (0, −1), (1, 2); y = 3x: (0, 0), (1, 3); y = 3x + 1: (0, 1), (1, 4). Same slope 3, so the lines are parallel; b moves the line up or down and is where it cuts the y-axis.
- (v) y = −2x − 3: (0, −3), (1, −5); y = −2x: (0, 0), (1, −2); y = 2x + 3: (0, 3), (1, 5). The first two are parallel (slope −2); the third has slope 2, so it rises and is not parallel to them.
Answer: a is the slope (its size gives the steepness, its sign whether the line rises or falls); b is the y-intercept (it shifts the line up or down). Lines with the same a are parallel: (iv), and the first two lines of (v).
Other exercises in this chapter
- Exercise Set 2.1 — 5 questions
- Exercise Set 2.2 — 7 questions
- Exercise Set 2.3 — 5 questions
- Exercise Set 2.4 — 4 questions
- Exercise Set 2.5 — 3 questions
- End-of-chapter exercises — 14 questions
← Introduction to Linear Polynomials: notes, practice and all exercises
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