text: # SOLUTION: Are the following lines parrallel, perpendicular, or neither. L1 2x+4y=5 L2 x+2y=4 thanks for any help it is greatly appreciated Heather
  
  Algebra ->  -> SOLUTION: Are the following lines parrallel, perpendicular, or neither. L1 2x+4y=5 L2 x+2y=4 thanks for any help it is greatly appreciated Heather      Log On
  
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  Question 107870: Are the following lines parrallel, perpendicular, or neither. L1 2x+4y=5 L2 x+2y=4
  thanks for any help it is greatly appreciated
  Heather
  
  Found 2 solutions by checkley71, jim_thompson5910:
  You can put this solution on YOUR website!
  TO ANSWER THIS PROBLEM WE NEED TO FIND THE SLOPES OF THESE TWO LINES.
  2X+4Y=15
  4Y=-2X+15
  Y=-2X/4+15/4
  Y=-X/2+15/4 THIS LINE HAS A SLOPE IS -1/2.
  X+2Y=4
  2Y=-X+4
  Y=-X/2+4/2
  Y=-X/2+2 THIS LINE HAS A SLOPE OF -1/2.
  THEREFORE THEY ARE PARALLEL LINES.
  
  You can put this solution on YOUR website!
  First convert 2x+4y=5 into slope intercept form
  
   Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)
  
  Now convert x+2y=4 into slope intercept form
  
   Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)
  
  Since the slope of 2x+4y=5 is and the slope of x+2y=4 is . This means the slopes of the two equations are equal. So the lines are parallel.
  
  Notice if we graph the two equations we get
  
  (note: if you need help with graphing, check out this solver)
  
  Graph of and
  
  and we can see that the two lines are parallel. So this verifies our answer.
explanation: The document contains a math question about determining if two given lines are parallel, perpendicular, or neither. It also includes two detailed solutions to the question, explaining the steps to find the slopes of the lines and concluding that the lines are parallel.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # SOLUTION: Are the following lines parrallel, perpendicular, or neither. L1 2x+4y=5 L2 x+2y=4 thanks for any help it is greatly appreciated Heather
  
  Algebra ->  -> SOLUTION: Are the following lines parrallel, perpendicular, or neither. L1 2x+4y=5 L2 x+2y=4 thanks for any help it is greatly appreciated Heather      Log On
  
   Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!
  
  Question 107870: Are the following lines parrallel, perpendicular, or neither. L1 2x+4y=5 L2 x+2y=4
  thanks for any help it is greatly appreciated
  Heather
  
  Found 2 solutions by checkley71, jim_thompson5910:
  You can put this solution on YOUR website!
  TO ANSWER THIS PROBLEM WE NEED TO FIND THE SLOPES OF THESE TWO LINES.
  2X+4Y=15
  4Y=-2X+15
  Y=-2X/4+15/4
  Y=-X/2+15/4 THIS LINE HAS A SLOPE IS -1/2.
  X+2Y=4
  2Y=-X+4
  Y=-X/2+4/2
  Y=-X/2+2 THIS LINE HAS A SLOPE OF -1/2.
  THEREFORE THEY ARE PARALLEL LINES.
  
  You can put this solution on YOUR website!
  First convert 2x+4y=5 into slope intercept form
  
   Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)
  
  Now convert x+2y=4 into slope intercept form
  
   Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Multiply both sides by Distribute Multiply Rearrange the terms Reduce any fractions So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)
  
  Since the slope of 2x+4y=5 is and the slope of x+2y=4 is . This means the slopes of the two equations are equal. So the lines are parallel.
  
  Notice if we graph the two equations we get
  
  (note: if you need help with graphing, check out this solver)
  
  Graph of and
  
  and we can see that the two lines are parallel. So this verifies our answer.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question about determining if two given lines are parallel, perpendicular, or neither. It also includes two detailed solutions to the question, explaining the steps to find the slopes of the lines and concluding that the lines are parallel.
  
  Label: question-and-answer