# 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.
The text contains a mathematical question about determining the relationship between two lines (parallel, perpendicular, or neither) and provides a detailed solution showing that the lines are parallel.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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.
user
The text contains a mathematical question about determining the relationship between two lines (parallel, perpendicular, or neither) and provides a detailed solution showing that the lines are parallel.

TYPE: SINGLE_QUESTION_WITH_ANSWER