Skills · Linear Equations · Systems of Equations

Writing a system from its graph

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. lines through (0, 4), (1, 1), (0, 3), (1, 5)4−67−3xy
  2. lines through (0, 3), (1, 2), (0, −2), (1, 1)7−34−6xy
  3. lines through (0, −2), (1, −4), (0, −3)6−43−7xy
  4. lines through (0, 2), (1, 4), (0, 4), (1, 2)7−35−5xy
  5. lines through (0, 1), (1, −2), (1, −1)7−35−5xy
  6. lines through (0, 2), (1, 5), (1, 3)5−57−3xy
  7. lines through (0, −2), (−1, 1), (0, 0), (1, 1)3−76−4xy
  8. lines through (0, 0), (1, 3), (0, 2), (1, 1)5−56−4xy

Answer key

  1. y < 2x + 3 and y > −3x + 4
  2. y ≤ 3x − 2 and y ≥ −x + 3
  3. y > −2x − 2 and y ≥ −x − 3
  4. y > 2x + 2 and y ≤ −2x + 4
  5. y > −2x + 1 and y ≥ −3x + 1
  6. y ≤ x + 2 and y ≤ 3x + 2
  7. y ≥ −3x − 2 and y ≥ x
  8. y ≥ −x + 2 and y ≥ 3x

Sample Sheet · Level 3

  1. lines through (0, 0), (1, −2), (0, 3), (1, 4)7−36−4xy
  2. lines through (0, −1), (1, 1), (0, −4), (−1, −2)3−75−5xy
  3. lines through (0, −4), (3, −5), (0, −2), (1, −3)5−53−7xy
  4. lines through (0, −3), (1, −2), (0, 2), (1, 2)7−34−6xy
  5. lines through (0, 3), (1, 5), (0, 2), (1, 2)4−66−4xy
  6. lines through (0, −3), (1, −2), (0, 4), (2, 3)7−36−4xy
  7. lines through (0, 3), (1, 3), (0, −2), (1, −1)7−36−4xy
  8. lines through (0, 3), (−1, 1), (0, 0), (2, 1)3−74−6xy

Answer key

  1. y > −2x and y > x + 3
  2. y > 2x − 1 and y ≤ −2x − 4
  3. y < −x − 2 and y ≥ −13x − 4
  4. y ≤ 2 and y ≥ x − 3
  5. y ≥ 2 and y ≥ 2x + 3
  6. y < −12x + 4 and y > x − 3
  7. y < 3 and y > x − 2
  8. y > 2x + 3 and y ≤ 12x

Make your own

Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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