Answer:
D
Step-by-step explanation:
We have the two linear equations:
[tex]\text{ Line 1: }y=3x+3[/tex]
[tex]\text{ Line 2: }y=-3x-5[/tex]
And we want to determine the relationship between them.
Let's go through each of the answer choices.
Parallel?
Remember that parallel lines have the same slopes.
The slope of Line 1 is 3, while the slope is Line 2 is -3.
Since they have different slopes, they are not parallel.
Perpendicular?
Perpendicular lines have slopes who are negative reciprocals of each other.
For example, the negative reciprocal of 2 will be -1/2. And the negative reciprocal of -1/2 is 2.
The slope of Line 1 is 3. The negative reciprocal of 3 is -1/3. This is not the slope of Line 2.
We can do it for Line 2 just to confirm. The slope of Line 2 is -3. The negative reciprocal of -3 is 1/3.
So, because their slopes are not negative reciprocals of each other, the two lines are not congruent.
Both?
No two lines can be both parallel and perpendicular simultaneously, so this is out of the question.
[N]either?
Yes indeed. They lines are neither parallel nor perpendicular, so this is our only choice.
And we're done!
