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

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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:
Answer by checkley71(8403)   (Show Source): 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.

Answer by jim_thompson5910(35256)   (Show Source): 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)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


Start with the given equation


Subtract 2x from both sides


Simplify


Divide both sides by 4 to isolate y


Break up the fraction on the right hand side


Reduce and simplify


The original equation (standard form) is equivalent to (slope-intercept form)


The equation is in the form where is the slope and is 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)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


Start with the given equation


Subtract 1x from both sides


Simplify


Divide both sides by 2 to isolate y


Break up the fraction on the right hand side


Reduce and simplify


The original equation (standard form) is equivalent to (slope-intercept form)


The equation is in the form where is the slope and is 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.
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