SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 4y = 12 L2 with equation 4x + y = 4

Algebra ->  Systems-of-equations -> SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x – 4y = 12 L2 with equation 4x + y = 4       Log On


   

Question 109407: Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 4y = 12
L2 with equation 4x + y = 4
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the slope of x – 4y = 12

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-4y=12 Start with the given equation


1x-4y-1x=12-1x Subtract 1x from both sides


-4y=-1x%2B12 Simplify


%28-4y%29%2F%28-4%29=%28-1x%2B12%29%2F%28-4%29 Divide both sides by -4 to isolate y


y+=+%28-1x%29%2F%28-4%29%2B%2812%29%2F%28-4%29 Break up the fraction on the right hand side


y+=+%281%2F4%29x-3 Reduce and simplify


The original equation 1x-4y=12 (standard form) is equivalent to y+=+%281%2F4%29x-3 (slope-intercept form)


The equation y+=+%281%2F4%29x-3 is in the form y=mx%2Bb where m=1%2F4 is the slope and b=-3 is the y intercept.






Now let's find the slope of 4x + y = 4

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)


4x%2B1y=4 Start with the given equation


4x%2B1y-4x=4-4x Subtract 4x from both sides


1y=-4x%2B4 Simplify


The original equation 4x%2B1y=4 (standard form) is equivalent to y+=+-4x%2B4 (slope-intercept form)


The equation y+=+-4x%2B4 is in the form y=mx%2Bb where m=-4 is the slope and b=4 is the y intercept.






Now multiply the slopes of 1%2F4 and -4 to get %281%2F4%29%28-4%29=-4%2F4=-1

Since the product of the two slopes is -1, the two slopes are perpendicular

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Are the following lines parallel, perpendicular, or neither?
L1 with equation x – 4y = 12
L2 with equation 4x + y = 4
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Write in slope-intercept form:
L1: y = (1/4)x-3; slope is 1/4
L2: y = -4x+4; slope is -4
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Since (14)*(-4)= 1- the lines are perpendicular.
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Cheers,
Stan H.