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

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) (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)

Start with the given equation

Subtract 1x 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 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)

Start with the given equation

Subtract 4x from both sides

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 multiply the slopes of and to get

Since the product of the two slopes is -1, the two slopes are perpendicular
Answer by stanbon(75887) (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.
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