Lesson 2 of 5 · Algebra
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A linear equation in two variables describes a line: every point on the graph is a pair that makes the equation true. The SAT tests whether you can move fluently between a line’s equation, graph and real-world meaning. That covers finding slopes and intercepts in any form, writing the line through given points, and interpreting budget and combination models.
These questions appear throughout both Math modules, as multiple choice and as SPR:
| Form | Typical stem |
|---|---|
| Slope or intercept | “What is the slope of the graph of in the xy-plane?” |
| Equation from a graph or points | “The graph of a line is shown. Which equation defines the line?” |
| Point on a line | “The point lies on the line with equation . What is ?” |
3 questions on linear equations in two variables. Every option is explained once you answer.
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The first 3 of 10 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.
What is the slope of the line through and ?
| Parallel or perpendicular | “Line is perpendicular to line and passes through …” |
| Context model | “Which equation represents this situation?” and “What is the best interpretation of the -intercept?” |
Easy versions ask you to read one feature. Hard versions chain two or three steps, such as finding a constant, then the slope, then an intercept. They may use letters instead of numbers (“”) or ask you to interpret a rearranged equation.
| Form | Equation | What you can read off immediately |
|---|---|---|
| Slope-intercept | slope ; -intercept | |
| Point-slope | slope ; the point | |
| Standard | slope ; -intercept ; -intercept |
Point-slope form hides a sign trap: passes through , because .
A fourth form appears occasionally: has intercepts and , so its slope is .
A point lies on a line exactly when its coordinates make the equation true. To find a missing coordinate, substitute the one you know and solve. To find a constant in the equation, substitute a point the line passes through.
When two kinds of items combine to a fixed total, such as tickets, budgets, calories or points:
y1 ~ m x1 + b to get the exact slope and intercept.y1 ~ m x1 + b turns any two points into an exact equation in seconds.