Answer:
The answer is PERPENDICULAR.
Explanation:
In order to find the answer, you should find the gradient of the equation, y = mx + b where m is the gradient :
1st equation,
-4y = -3x - 3
y = (-3/-4)x + (-3/-4)
= (3/4)x + 3/4
m = 3/4
2nd equation,
-12x = 9y + 8
9y = -12x - 8
y = (-12/9)x + (-8/-9)
= (-4/3)x + 8/9
m = -4/3
When the equations are parallel, the gradient should be same. But in these 2 equation, they have different gradient so they are NOT parallel.
When 2 equations are perpendicular, their gradient should be opposite to each other using the formula to check, m1×m2 = -1, where m1 is the gradient from 1st equation and m2 is from 2nd equation :
m1 = 3/4
m2 = -4/3
m1 × m2 = 3/4 × -4/3
= -1
So when these 2 gradient are multiplied, you get -1 which means these 2 equations are PERPENDICULAR.