Introduction to Linear Polynomials

A collection of vocabulary flashcards based on the Grade 9 lecture notes regarding algebraic expressions, types of polynomials, and linear patterns.

Variable

An alternate word for letter-numbers used in algebraic expressions, such as $x$ and $y$.

Terms

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

Coefficients

The numerical factors in the terms of an expression, such as the numbers $4$ and $5$ in the expression $4x + 5y + 3$.

Constant

A number in an algebraic expression that does not change and is not multiplied by a variable, such as the number $3$ in $4x + 5y + 3$.

Univariate Polynomials

Algebraic expressions involving only one variable and its powers, also known as one-variable polynomials.

Degree of a Polynomial

The highest power of the variable present in a polynomial.

Cubic Polynomial

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

Quadratic Polynomial

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

Linear Polynomial

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

Constant Polynomial

A polynomial with a degree of $0$, which can be written as a constant multiplied by a variable to the power of $0$, such as $8x^0$.

Linear Equation

An equation formed when a linear polynomial in one variable is equated to a constant.

Linear Pattern

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

Linear Growth

A linear pattern where a quantity increases by a fixed amount over equal intervals, represented by a straight line with a positive slope.

Linear Decay

A linear pattern where a quantity decreases by a fixed amount over equal intervals, represented by a straight line with a negative slope.

Linear Relationship

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

Slope

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

Y-intercept

The value $b$ in the equation $y = ax + b$, representing the point $(0, b)$ where the line cuts the y-axis.

Parallel Lines

Lines that have the same slope $a$ but different y-intercepts $b$.