SOLUTION: 6. Are the following pairs of line parallel, perpendicular, or neither. L1 with equation x + 2y = 4 L2 with equation 2x + 4y =5

Algebra ->  Graphs -> SOLUTION: 6. Are the following pairs of line parallel, perpendicular, or neither. L1 with equation x + 2y = 4 L2 with equation 2x + 4y =5       Log On


   

Question 121214: 6. Are the following pairs of line parallel, perpendicular, or neither.

L1 with equation x + 2y = 4
L2 with equation 2x + 4y =5
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First convert the standard equation x%2B2y=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.





Now convert the standard equation 2x%2B4y=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.







Since the two slopes are both m=-1%2F2, this means that the two slopes are equal. This also means that the two lines are parallel



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Answer:

So the lines x+%2B+2y+=+4 and 2x+%2B+4y+=5 are parallel.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First find the slope of each of the two lines by rewriting the equatins in slope-intercept form: y+=+mx%2Bb.
L1: y+=+-%281%2F2%29x%2B2
L2: y+=+-%281%2F2%29x%2B5%2F4
Now compare with:
y+=+mx%2Bb and you can see that in both equations, m+=+-%281%2F2%29
The slopes, m, are equal so the lines are parallel.