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

Hi Lindsey;

x - 3y = 6 and y = 3x + 2

The second equation is in the format of...

y=mx+b, m is the slope.

Let's convert the first equation...

x - 3y = 6

Let's subtract x from both sides...

-x+x-3y=-x+6

-3y=-x+6

Let's divide both sides by -3...

(-3y)/-3=(-x+6)/-3

A negative number divided by a negative number results in a positive number.

y=(1/3)x-2

 

The first equation has a slope of 1/3.

The second equation has a slope of 3.

Perpendicular equations must have slopes which are negative-inverses of the other.

These are not.

C, Neither

 

For the equations to be parallel, the slopes must be equal. x-3y=6 converts to y=1/3x-2, having a slope of 1/3

y=3x+2, has a slope of 3 so since they do not equal, they are not parallel.

 

For two lines to be perpendicular the slope must be the inverse negative slope of the other. Since that is not the case in this situation, it is not perpendicular either.