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

Algebra ->  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

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

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(21685) 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)


1%2Ax-4%2Ay=12Start with the given equation



-4%2Ay=12-1%2Ax Subtract 1%2Ax from both sides

y=%28-1%2F4%29%2812-1%2Ax%29 Multiply both sides by -1%2F4

y=%28-1%2F4%29%2812%29%2B%281%2F4%29%281%29x%29 Distribute -1%2F4

y=-12%2F4%2B%281%2F4%29x Multiply

y=%281%2F4%29%2Ax-12%2F4 Rearrange the terms

y=%281%2F4%29%2Ax-3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F4 (the slope) and b=-3 (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)


4%2Ax%2B1%2Ay=4Start with the given equation



1%2Ay=4-4%2Ax Subtract 4%2Ax from both sides

y=%281%29%284-4%2Ax%29 Multiply both sides by 1

y=%281%29%284%29-%281%29%284%29x%29 Distribute 1

y=4-%284%29x Multiply

y=-4%2Ax%2B4 Rearrange the terms

y=-4%2Ax%2B4 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-4 (the slope) and b=4 (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(48568) 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
----------------
Write in slope-intercept form:
L1: y = (1/4)x-3; slope is 1/4
L2: y = -4x+4; slope is -4
-------------
Since (14)*(-4)= 1- the lines are perpendicular.
==============
Cheers,
Stan H.