Determine whether the lines are parallel, perpendicular or neither:
line 1: 4y−12=3x
line 2: 2y−1.5x=−14

For this case we have to by definition:

If two lines are parallel then their slopes are equal.

If two lines are perpendicular then the product of their slopes is equal to -1.

We have the following equations:

We manipulate the equation to convert it into the slope-intersection form

Where:

m: It's the slope

y: It is the cut-off point with the y axis.

So:

From the second equation given we have:

We manipulate:

It is observed that the slopes are equal, so the lines are parallel,

The lines are parallel.

step-by-step explanation:

i am not sure sorry : c

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: