SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 with equation x � 6y = 12 L2 with equation 6x + y = 6

Question 111294: Are the following lines parallel, perpendicular, or neither?
L1 with equation x � 6y = 12
L2 with equation 6x + y = 6

Found 2 solutions by kmcruz09, MathLover1:
Answer by kmcruz09(38) (Show Source): You can put this solution on YOUR website!
The line equations must first be converted to the standard form where m is the slope.
So,

Then

Lines that are perpendicular to each other have negative reciprocal slopes, while lines that are parallel to each other have the same slopes.
Since we already changed the equations to the standard form, we can now take the slope.
For the first line, , the slope is as I said before, the literal coefficient of x is the slope in the standard form. Then for the second line, , the slope is -6.
and are negative reciprocals, therefore, the two lines are perpendicular to each other.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Solve the System of Equations by Graphing

Start with the given system of equations:

In order to graph these equations, we need to solve for y for each equation.

So let's solve for y on the first equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

Since you have and , and perpendicular lines have slope that are negative reciprocals , then:

�so, your lines are perpendicular

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