Question

The equations of two lines are x - 3y = 6 and y = 3x + 2. Determine if the lines are parallel, perpendicular or neither.

Answer 1

First, put the equations in slope intercept form 

x - 3y = 6
-x        -x 
-3y = -x + 6 ( Divide both sides by -3)
y = -1/3 - 2

So the two equations are
y = -1/3x - 2
y = 3x + 2

Because the slopes are opposite reciprocals they are perpendicular 

Hope this helps :)

Answer 2

Answer:

neither

Step-by-step explanation:

The equations of two lines are $x - 3y = 6$and $y = 3x + 2$

When the slopes of two lines are equal then the lines are parallel.

When the slopes of two lines are negative reciprocal of one another then the lines are perpendicular to each other.

We solve for y and check the slope of two equations

$x - 3y = 6$ (subtract x on both sides)

$-3y =-x+6$

Now divide by -3 on both sides

$y=\frac{1}{3} x -2$

Slope of this line is $\frac{1}{3}$

$y = 3x + 2$

Slope of second line is 3

Slopes of both lines are not negative reciprocal of one another

So they are neither