9-10 Writing Equations
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9-10 Writing Equations

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9-10 Writing Equations 9-10 Writing Equations Presentation Transcript

  • 9-10 Writing Equations Algebra and Functions 1.5
  • Skills Needed:
  • Skills Needed:Recognizing patterns
  • Skills Needed:Recognizing patterns+3x y402
  • Skills Needed: Recognizing patternsBefore: You were given the rule. +3 x y 4 0 2
  • Skills Needed: Recognizing patternsBefore: You were given the rule. + 3 x y 4 7 0 3 2 5
  • Skills Needed: Recognizing patternsBefore: You were given the rule. + 3 ? x y x y 4 7 2 7 0 3 3 8 2 5 4 9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND THE RULE. + 3 ? x y x y 4 7 2 7 0 3 3 8 2 5 4 9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND THE RULE. + 3 ? x y x y 4 7 2 7 2+5=7 0 3 3 8 2 5 4 9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND THE RULE. + 3 ? x y x y 4 7 2 7 2+5=7 0 3 3 8 3+5=8 2 5 4 9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND THE RULE. + 3 ? x y x y 4 7 2 7 2+5=7 0 3 3 8 3+5=8 2 5 4 9 4+5=9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND THE RULE. + 3 ? x y x y 4 7 2 7 2+5=7 0 3 3 8 3+5=8 2 5 4 9 4+5=9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND THE RULE. + 3 x y x y 4 7 2 7 2+5=7 0 3 3 8 3+5=8 2 5 4 9 4+5=9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND THE RULE. + 3 + 5 x y x y 4 7 2 7 2+5=7 0 3 3 8 3+5=8 2 5 4 9 4+5=9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND The Rule! THE RULE. + 3 + 5 x y x y 4 7 2 7 2+5=7 0 3 3 8 3+5=8 2 5 4 9 4+5=9
  • Skills Needed: Recognizing patternsBefore: You were Today: You find a given the rule. pattern to FIND The Rule! THE RULE. + 3 + 5 x y x y 4 7 2 7 2+5=7 0 3 3 8 3+5=8 2 5 4 9 4+5=9 The equation is written y = x + 5.
  • x -3 -2 -1 0 1 2 3y -6 -5 -4 -3 -2 1 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ?-3 -6-2 -5-1 -4 0 -3 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? Use number lines to help find-3 -6 a pattern to identify the RULE.-2 -5-1 -4 0 -3 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ?-3 -6-2 -5-1 -4 0 -3 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ?-3 -6-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7-1 -4 0 -3 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ?-3 -6-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7-1 -4 0 -3 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7-1 -4 0 -3 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7-1 -4 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7-1 -4 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 -2 2 -1 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 -2 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 -2 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 -2 left - 3 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 0
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 -2 left - 3 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 0 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 -2 left - 3 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 0 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 ? moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 -2 left - 3 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 3 0 left - 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 -2 left - 3 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 3 0 left - 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 - 3 moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 -2 left - 3 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 3 0 left - 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y -6 -5 -4 -3 -2 1 0 - 3 moves-3 -6 left - 3-2 -5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves-1 -4 left - 3 0 -3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 -2 left - 3 2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 3 0 left - 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 The equation is written y = x - 3.
  • x -3 -2 -1 0 1 2 3y 2 3 4 5 6 7 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? -3 2 -2 3 -1 4 0 5 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? Use number lines to help find -3 2 a pattern to identify the RULE. -2 3 -1 4 0 5 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? -3 2 -2 3 -1 4 0 5 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? -3 2 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 -1 4 0 5 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? -3 2 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 -1 4 0 5 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 -1 4 0 5 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 -1 4 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 -1 4 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 6 2 7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 6 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 1 6 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 8
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 3 8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 3 8 right -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 ? moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +8 moves 3 8 right -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +8 moves 3 8 right -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 + 5 moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +8 moves 3 8 right -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5
  • Rewrite x -3 -2 -1 0 1 2 3vertically. y 2 3 4 5 6 7 8 + 5 moves -3 2 right +5 -2 3 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves -1 4 right +5 0 5 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 moves 1 6 right +5 2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +8 moves 3 8 right -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5 The equation is written y = x + 5.
  • Write an equation to describe the relationship between x and y.
  • Write an equation to describe the relationship between x and y.x y-2 8-1 90 101 112 12
  • Write an equation to describe the relationship between x and y.x y x y-2 8 -2 -4-1 9 -1 -30 10 0 -21 11 1 -12 12 2 0
  • Write an equation to describe the relationship between x and y.x y x y x y-2 8 -2 -4 -2 4-1 9 -1 -3 -1 50 10 0 -2 0 61 11 1 -1 1 72 12 2 0 2 8
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10 y=x-2
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10 y=x-2
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10 y=x-2
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10 y=x-2 y=x+6
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10 y=x-2 y=x+6
  • Write an equation to describe the relationship between x and y. x y x y x y -2 8 -2 -4 -2 4 -1 9 -1 -3 -1 5 0 10 0 -2 0 6 1 11 1 -1 1 7 2 12 2 0 2 8y = x + 10 y=x-2 y=x+6