Linear equations in two variables
Read the equation form first to identify slope, intercepts, and what the line means.
Core Idea
A linear equation in two variables defines a straight line; every point on that line is a solution, and the equation's form tells you the slope and position of the line.
Understanding
Read the form first. A linear equation in two variables is a line, and the form tells you what to notice.
𝑦 = 𝑚 𝑥 + 𝑏 𝐴 𝑥 + 𝐵 𝑦 = 𝐶 𝑦 − 𝑦 1 = 𝑚 ( 𝑥 − 𝑥 1 )
The SAT tests whether you can move between these forms, read slope and intercepts, and use them in context. Parallel lines have the same slope, and perpendicular lines have negative reciprocal slopes.
Concept Guides
6Work with linear equations in forms such as Ax+By=C and y=mx+b.
Convert between line forms to reveal slope, intercepts, or a known point.
Write the equation of a line given points, slope, or a graph.
Find a slope and a point, then use point-slope form to write the equation.
Compute slope and intercepts from an equation or graph.
Read slope and intercepts directly from slope-intercept form, standard form, or a graph.
Find one variable value given the other and interpret in context.
Substitute the known value, solve, and interpret the result in context.
Identify lines parallel/perpendicular using slope relationships.
Parallel lines match slopes; perpendicular lines use negative reciprocal slopes.
Connect models, tables, graphs, and equations for linear relationships.
Tables, graphs, equations, and word problems can all encode the same linear rule.