Algebra dictionary

THIS IS A MUST CHECK IF YOU ARE NEW TO ALGEBRA

Constant: A value that does not change, is independent, and is not obscured.

Examples: 3, 6, 8, 14, 30, pi

Variable: A value that can change, often across infinite values. Often solved for in algebraic problems. Almost always denoted with a letter, especially in algebra. Most common letters used are x, y, z, a, b, c, n. 

Dependent Variables are variables that change based on the value of the independent variable. In most functions and equations, "y" is the dependent variable that depends on "x".

Independent Variables are variables that change others, not changing based on others. In most functions and equations, "x" is the independent variable. An example of an independent variable is "t", in d=t*s where distance depends on the time and speed. 

Expression: A mix of constants and variables that are joined by operations

Examples: x^2, x+5, a+b+c+abc, xy+yz

Equation: Two or more expressions joined by an equal sign signifying that the two expressions are equal. Usually, the variables need to be solved for, and you can learn how to do that in our Expressions and Equations page. 

Term: Any part of an expression or equation that is a collection of variables and a constant. Terms are separated by addition and subtraction. Two variables multiplying or dividing each other can be seen as two terms, but in most contexts, we like to see them as one term together.

Examples: In the equation 4x+5/x=3, the terms are 4x, 5/x, and 3. In the equation x^5 + x^4 + x^3 + x^2 + x + 1 + 1/x = x^6, the terms are x^5, x^4, x^3, x^2, x^1, 1, 1/x, and x^6. In the equation abc = (2a+3b)/c - 2ac + 2ba, the terms are abc, (2a+3b)/c , -2ac, and 2ba. Note how if a term is subtracted, the term is negative.

Coefficient: The constant part of a term. 

Like Terms: Any two terms that have the same variable part but not necessarily the same constant coefficients. They can be added together to form one larger term with equal value.

Example: 3a and 4a are like terms, x^6 and (x^6)/2 are like terms, x and 1/x are not like terms.

The variable "m" in equations likely means slope while b likely means the y-intercept. A number at the bottom right of a variable means the same variable with a different value under different circumstances (e.g. two different outputs when the input is altered)

ab means a*b or a multiplied by b.

Relation: A pairing of input constants and output constants.

Example: 

Function: Any relation that has exactly one output for each input.

f(x): A function f applied to a variable x. Usually there is an equal sign that explains the function. There is a section on solving functions

Examples: f(x)=x^2+2x+1

i : The number that when squared equals -1. Check our complex numbers section for more information

Linear equation: Any equation that does not include any terms with a variable that are put at a power greater than 1 or any terms with a fractions with a variable as the denominator. This is so the expressions on either side of the equation will be lines when graphed on the coordinate plane.  

Examples: 4c-4=0, n=2n+300, 3n=0