Linear Functions and Slope
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalA linear function is a straight line with a rule behind it: a constant rate turns each input into an output, and the equation carries the rate and the starting value side by side. The algebra is short. The points leak in the reading, the slope reported when the intercept was asked or the reverse, a perpendicular slope with only half the move done, flipped without negating or negated without flipping, and function notation read as multiplication instead of a value.
These patterns aren't really about whether you can work with a line. They're about whether you read the feature the question actually named, whether you did both halves of the perpendicular move, the flip and the sign, and whether you treated f(3) as the output of the function at 3, not f times 3.
The work
4 ways in · any order
Lesson
Linear Functions and Slope
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Read slope and intercept off an equation or a graph, build a perpendicular slope with both moves done, and evaluate function notation as a substitution, not a product. The lesson works the method and the three patterns that derail it, and it saves the notation trap for last: f(3) multiplied out instead of looked up.
Diagnostic
10-item topic check
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Ten items across the three patterns: swapping slope and intercept, half-changing a perpendicular slope, and reading a function value as multiplication. A mix of equation reads, graph reads, and function-value questions. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.