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 ->  Linear-equations -> 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


   

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) About Me  (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) About Me  (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)


2x%2B4y=5 Start with the given equation


2x%2B4y-2x=5-2x Subtract 2x from both sides


4y=-2x%2B5 Simplify


%284y%29%2F%284%29=%28-2x%2B5%29%2F%284%29 Divide both sides by 4 to isolate y


y+=+%28-2x%29%2F%284%29%2B%285%29%2F%284%29 Break up the fraction on the right hand side


y+=+%28-1%2F2%29x%2B5%2F4 Reduce and simplify


The original equation 2x%2B4y=5 (standard form) is equivalent to y+=+%28-1%2F2%29x%2B5%2F4 (slope-intercept form)


The equation y+=+%28-1%2F2%29x%2B5%2F4 is in the form y=mx%2Bb where m=-1%2F2 is the slope and b=5%2F4 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)


1x%2B2y=4 Start with the given equation


1x%2B2y-1x=4-1x Subtract 1x from both sides


2y=-1x%2B4 Simplify


%282y%29%2F%282%29=%28-1x%2B4%29%2F%282%29 Divide both sides by 2 to isolate y


y+=+%28-1x%29%2F%282%29%2B%284%29%2F%282%29 Break up the fraction on the right hand side


y+=+%28-1%2F2%29x%2B2 Reduce and simplify


The original equation 1x%2B2y=4 (standard form) is equivalent to y+=+%28-1%2F2%29x%2B2 (slope-intercept form)


The equation y+=+%28-1%2F2%29x%2B2 is in the form y=mx%2Bb where m=-1%2F2 is the slope and b=2 is the y intercept.




Since the slope of 2x+4y=5 is -1%2F2 and the slope of x+2y=4 is -1%2F2. 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%28500%2C500%2C-10%2C10%2C-10%2C10%2C%285-2x%29%2F4%2C%284-x%29%2F2%29 Graph of 2x%2B4y=5 and x%2B2y=4

and we can see that the two lines are parallel. So this verifies our answer.