Linear Equations in Two Variables
Finding slopes, intercepts, and working with parallel and perpendicular lines
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Two variables and one equation that describes a line. The SAT asks you to find slopes, intercepts, and meaning from equations, graphs, and word problems.
Why this matters
Most questions in this skill never ask you to solve. They ask you to interpret a coefficient, build an equation from a word problem, find a parallel or perpendicular slope, extract an intercept, or read properties from a graph. There are five question types, each with its own method.
The five patterns
Interpret Models
A linear equation models a real-world situation. You identify what a coefficient, variable, constant, product term, or ordered pair means in context. No solving — just matching pieces to roles.
›Word Problems
Build the correct equation from a scenario with two categories and a total, or substitute a given value and solve. The top pitfall: swapping which coefficient goes with which variable.
›Parallel & Perpendicular
Find the slope of a line parallel or perpendicular to a given line. Parallel means same slope. Perpendicular means negative reciprocal. Harder versions require rearranging from standard form first.
›Properties from Equations
Extract slope, y-intercept, or x-intercept from an equation. If it is not already in y = mx + b form, rearrange it. Translations (vertical shifts) also show up here.
›Properties from Data
Find slope, intercepts, or the equation from a graph or table. Pick two clear points, compute the slope, then back-solve for b. Constants in the table cancel when you take differences.