Desmos Calculator Mastery • Lesson 6 of 7

Intersection Finding

Solve equations and systems by graphing both sides and reading where they cross.

A huge share of SAT questions reduce to “where do two graphs meet?” To solve 2x + 1 = -x + 7, graph y = 2x + 1 and y = -x + 7 on separate rows, then turn on key points: the calculator marks the crossing. Its x-coordinate solves the equation; the full (x, y) solves a system.

  1. Type y = 2x + 1 on one row.A rising line appears.
  2. Type y = -x + 7 on the next row.A second line appears in a new colour.
  3. Tick key points.The intersection is marked at (2, 5), so x = 2.
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If you see no crossing, the window may be too small — zoom out. Truly parallel lines never meet, which means the equation has no solution.
Try it liveFind where two lines meet
  • y = 2x + 1 is loaded. Add a second row: y = -x + 7.
  • Tick key points to mark the intersection (2, 5).
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