Determine the Quadrants

Yes, your logic for question #2 is correct.

For question #1 try the following points.

(1,1)
(1,-1)
(-1, -1)
(-1, 1)

Are you saying the answer for question 1 is all 4 quadrants?

No, I am not saying it is all 4 quadrants.

Take the first point I suggest... (1,1). Does that meet the condition x + y = 0? Is there any point in quadrant 1 that meets that condition?

For question #1 try the following points.

(1,1)
(1,-1)
(-1, -1)
(-1, 1)

x + y = 0

Plugging in the point (1,1), I get 1 + 1 = 0, which is a false statement.

Plugging in the point (1, -1), I get 1 - 1 = 0, which is a true statement.

Plugging in the point (-1, -1), I get -1 - 1 = 0, which is a false statement.

Plugging in the point (-1, 1), I get - 1 + 1 = 0, which is a true statement.

Answer: For x + y = 0, points in the form (x, y) are located in quadrants 2 and 4.

Yes, that's correct.

You should confirm a few more points in each quadrant and you certainly should find a few more points that match the equalities in the second and fourth quadrant.

But yes! I think you have it.

Thanks. I love math. I graduated from college in 1994 but recently decided to revisit precalculus. Are you willing to take this journey with me? I need someone to help me as I go through the textbook. I am not a student. However, I have several college degrees in areas other than mathematics. You say?