Graphing Linear Equations and Ordered Pairs

Graphing the Equation

  • The equation to graph is:
    1−3x=y1 - 3x = y
      - This can be rewritten in standard slope-intercept form:
    y=−3x+1y = -3x + 1

Finding Points on the Graph

To determine which ordered pair lies on the graph of the equation, we will substitute the x-coordinates from each option into the equation and see if the resulting y-coordinate matches.

Option A: (5, -2)

  • Substitute x=5x = 5 into the equation:
    y=−3(5)+1y = -3(5) + 1
    y=−15+1y = -15 + 1
    y=−14y = -14
  • Ordered pair (5, -2) does NOT satisfy the equation.

Option B: (2, 5)

  • Substitute x=2x = 2 into the equation:
    y=−3(2)+1y = -3(2) + 1
    y=−6+1y = -6 + 1
    y=−5y = -5
  • Ordered pair (2, 5) does NOT satisfy the equation.

Option C: (-2, -5)

  • Substitute x=−2x = -2 into the equation:
    y=−3(−2)+1y = -3(-2) + 1
    y=6+1y = 6 + 1
    y=7y = 7
  • Ordered pair (-2, -5) does NOT satisfy the equation.

Option D: (2, -5)

  • Substitute x=2x = 2 into the equation again (note: previously we checked (2, 5)):
    y=−3(2)+1y = -3(2) + 1
    y=−6+1y = -6 + 1
    y=−5y = -5
  • Ordered pair (2, -5) satisfies the equation.

Conclusion

  • The correct answer is: D, (2, -5), as this ordered pair is on the graph of the equation y=−3x+1y = -3x + 1 which is derived from the original equation.