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Class 9 Introduction to Linear Polynomials: cheat sheet
CBSE Mathematics. A linear polynomial ax + b has degree 1. Its graph is a straight line; a tells how steep it is and b where it crosses the y-axis.
Key ideas
- A linear polynomial is ax + b with a ≠ 0; its degree is 1.
- The value of p(x) at x = k is found by putting k in place of x.
- The zero of ax + b is the x that makes it 0: x = −b/a. A linear polynomial has exactly one zero.
- The graph of y = ax + b is a straight line. The zero is where the line crosses the x-axis.
- a is the slope: y changes by a each time x goes up by 1. b is the y-intercept.
- Lines with the same slope are parallel and never meet.
- Everyday rules such as “fixed charge + rate × quantity” are linear: fare = 30 + 12x.
Remember
| Zero of ax + b | x = −b/a |
| Slope through (x₁, y₁) and (x₂, y₂) | (y₂ − y₁) ÷ (x₂ − x₁) |
| Line | y = ax + b: slope a, y-intercept b |
Watch out
- Getting the sign of the zero wrong: the zero of 2x + 6 is −3, not 3.
- Mixing up the slope (the number with x) and the intercept (the constant).
- Thinking a line with a bigger intercept is steeper.
Worked example
Are the lines y = 4x + 7 and y = 4x + 15 parallel? Do they meet?
Working: same slope 4, different y-intercepts 7 and 15
Answer: parallel; they never meet
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