Introduction to Linear Polynomials

Vocabulary flashcards covering the fundamental concepts of algebraic expressions, various types of univariate polynomials, linear patterns, and their graphical representations as discussed in the Grade 9 Ganita Manjari lecture notes.

Algebraic expression

A combination of numbers, variables, and operation symbols such as $2x^2 + 5xy - 3y^2$.

Terms

The individual parts of an algebraic expression; for example, in $4x + 5y + 3$, the terms are $4x$, $5y$, and $3$.

Variables

The letter-numbers used in an expression, such as $x$ and $y$, that represent unknown quantities.

Coefficients

The numbers multiplying variables in an algebraic expression; for example, in $4x + 5y + 3$, the numbers $4$ and $5$ are the coefficients.

Constant

A fixed number in an algebraic expression that does not have a variable attached to it, such as the number $3$ in $4x + 5y + 3$.

Univariate Polynomials

Also known as one-variable polynomials, these are algebraic expressions involving only one variable and its powers.

Univariate

A term meaning "having one variable".

Degree

The highest power of the variable in a polynomial expression.

Linear Polynomial

A polynomial of degree $1$, such as $3z + 7$.

Quadratic Polynomial

A polynomial of degree $2$, such as $x^2 + 5x + 1$.

Cubic Polynomial

A polynomial of degree $3$, such as $5y^3 + y^2 + 2y - 1$.

Constant Polynomial

A polynomial of degree $0$, consisting of only a constant number, such as $8$ (which can be written as $8x^0$).

Linear pattern

A sequence of numbers where the difference between two consecutive terms is constant.

Linear equation

The result of equating a linear polynomial in one variable to a constant, such as $2x + 10 = 64$.

Function

An input-output process where an expression describes the relationship between an input value and a corresponding output value.

Linear growth

A linear pattern where a quantity increases by a constant amount over equal intervals.

Linear decay

A linear pattern where a quantity decreases by a constant amount over equal intervals.

Linear relationship

The relationship between two variables $x$ and $y$ that can be expressed as $y = ax + b$.

Slope

The constant $a$ in the linear equation $y = ax + b$, representing the steepness of the line and the constant difference between consecutive terms.

y-intercept

The point where a straight line cuts the y-axis, represented by the value $b$ in the equation $y = ax + b$, occurring at the point $(0, b)$.

Parallel lines

Lines that have equal slopes but different y-intercepts.