# Determine if the lines y= 3(x-2) and 2y = 6x -9 are parallel.

Two parallel do not intersect.

Now, the lines we have are:

y= 3(x-2) and 2y = 6x -9

2y = 6x -9

=> y = ( 6x  - 9)/2

=> y = 3x - 9/2

Now we see that y= 3(x-2) => y - 3x = -6 and y =...

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Two parallel do not intersect.

Now, the lines we have are:

y= 3(x-2) and 2y = 6x -9

2y = 6x -9

=> y = ( 6x  - 9)/2

=> y = 3x - 9/2

Now we see that y= 3(x-2) => y - 3x = -6 and y = 3x - 9/2 => y - 3x = -9/2 are two non - intersecting lines.

Therefore they are parallel.

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Given the lines:

y= 3(x-2)

2y = 6x -9

We need to determine if the lines are parallel.

First we will rewrite he equations of the lines into the slope form.

If the slopes are equal, then the lines are parallel.

==> y= 3(x-2)

==> y= 3x -6 ==> the slope m1 = 3

2y = 6x -9

Divide by 2:

==> y= 3x - 4.5 ==> the slope m2= 3

Then, we notice that m1= m2.

Then, the lines are parallel.

Approved by eNotes Editorial Team