PSAT 8/9 Math — Algebra: Linear Relationships and Inequalities

Linear Equation in One Variable

An equation where the variable appears to the first power and results in a single solution.

Properties of Equality

Rules stating that you can add/subtract the same number or multiply/divide by the same nonzero number on both sides of an equation.

Solving an Equation

Finding the value of a variable that makes both sides of an equation equal.

No Solution

Occurs when simplifying an equation leads to a false statement.

Infinitely Many Solutions

Occurs when an equation simplifies to a true statement, meaning any value for the variable is acceptable.

Standard Form of a Linear Equation in Two Variables

A representation of a linear equation in the form Ax + By = C.

Slope-Intercept Form

A representation of a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Linear Function

A function with a rule that creates a straight-line graph.

Function Notation

A way to denote functions, such as f(x) = mx + b, indicating the output of the function for input x.

Slope

The change in y divided by the change in x between two points on a line.

y-Intercept

The value of y when x is 0 in the slope-intercept form of a linear equation.

System of Linear Equations

Two or more linear equations that are solved simultaneously.

Substitution Method

A method to solve a system by substituting one equation into another.

Elimination Method

A method to solve a system by adding or subtracting equations to eliminate a variable.

Linear Inequality

An inequality that compares linear expressions using symbols like

Boundary Line

The line that represents the equality part of a two-variable inequality.

Shaded Region

The area of the graph showing all possible solutions to a linear inequality.

Compound Inequality

An inequality that involves two inequalities, often expressed as a range of values.

Test Point Method

A technique for determining which side of a boundary line to shade in graphing inequalities.

Graphing Inequalities

The process of representing solutions of inequalities on the coordinate plane.

Vertical Line Test

A method to determine if a relation is a function, based on whether vertical lines intersect a graph at more than one point.

Linear Model

A representation of a real-world scenario using a linear equation or function.

Ordered Pair Solution

A solution to a system of equations represented as (x, y) that satisfies both equations.

Intercepts

Points where a line crosses either the x-axis (x-intercept) or the y-axis (y-intercept).

Opposite Operations

Actions that undo each other, such as addition and subtraction, used to isolate a variable in an equation.

Checking Solutions

The verification process to ensure that a solution satisfies the original equation.

Horizontal Line Test

A test to determine if a function is one-to-one, based on whether horizontal lines intersect the graph at more than one point.