SAT Algebra Explained — Complete Study Guide

A linear equation is an equation where the variable appears to the first power only, producing a straight-line graph. Solving it means finding the specific value of the variable that makes the equation true.

Equations that require more than one operation to solve, often involving distribution, combining like terms, and working across both sides of the equals sign.

Linear equations where the coefficients or constants are fractions or decimals, requiring additional steps to solve cleanly.

A linear function is a relationship between two variables where the change in the output is constant for every unit change in the input, always producing a straight-line graph. Written as f(x) = mx + b or y = mx + b.

Slope measures the steepness and direction of a line — it is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically: m = (y₂ - y₁) / (x₂ - x₁).

The equation of a line written as y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

Reading and extracting meaningful mathematical and real-world information from graphs, including identifying intercepts, slope, trends, intersections, and the behavior of a function.

A set of two or more linear equations sharing the same variables. The solution is the point (or points) where all equations are simultaneously satisfied — where all lines intersect.

A method for solving systems of equations where you solve one equation for one variable, then substitute that expression into the other equation to solve for the remaining variable.

A method for solving systems of equations where you add or subtract the equations (sometimes after multiplying) to eliminate one variable, leaving a single-variable equation to solve.

Real-world scenarios that require setting up and solving a system of two equations because two unknown quantities are described by two separate conditions.

A mathematical statement that compares a linear expression to a value using inequality signs (<, >, ≤, ≥), representing a range of solutions rather than a single value.

Representing the solutions of a linear inequality on a coordinate plane as a shaded half-plane, with a boundary line separating solutions from non-solutions.

Two or more linear inequalities considered simultaneously. The solution is the overlapping region (intersection) of all individual shaded regions — every point that satisfies ALL inequalities at once.