The scariest-looking questions on the test are stories: two gyms, two runners, two burning candles. Every one of them is secretly the same picture — two lines and a crossing.
The move: Turn each story into a line, tap the crossing.
Why it works: Each “story” is one relationship growing over time; graphing both makes “when are they equal?” a visible point instead of an equation to wrestle.
The pattern
- Write each quantity as y = …
- Graph both
- Tap the intersection → answer the question
Worked example: Gym A costs $30/month. Gym B costs $20/month plus a $60 sign-up fee. After how many months do they cost the same?
- Each gym's total cost is a line.
y=30x,y=20x+60 - Tap the intersection: (6, 180). Equal cost at 6 months ($180 each).
- Every “when are they equal” story ends at an intersection point.
Worked example 2: Runner A runs at 8 mph. Runner B starts half an hour later at 10 mph. How long has B been running when B catches A?
- Distance graphs, with x = time since A started. B's line starts late:
y=8x,y=10(x-0.5) - They meet at (2.5, 20) — 2.5 hours on A's clock, 20 miles out.
- But the question asks for B's running time: 2.5 − 0.5 = 2 hours. Tap the graph, then reread the question.
Remember it on test day
Two stories, two lines. That's the whole cue — say it when you see this question type and the steps follow.
When this isn't the move
Stories with three phases or changing rates may need a piecewise setup first — translate carefully before graphing.
Drill it until it's reflex
This move is one of Desvantage's 18 training modules: a plain-English lesson, a type-it-yourself walkthrough inside a live Desmos calculator, and a 100-question drill bank that deals ten fresh questions per round. The first two modules — plus the 12-question diagnostic — are free.