The point of the form (a, −a) always lies on the line:

Correct answer: x + y = 0. For (a, −a), x + y = a + (−a) = 0, so every such point lies on x + y = 0.

Background: For the point (a, −a), the x- and y-coordinates are opposites, so their sum is always zero.

• x = a: x = a holds only for one specific value of a, not for every such point.
• y = x: y = x holds only when a = 0.
• y = −a: y = −a is a horizontal line for one specific a, not all such points.

Did you know? Examples are (1, −1), (2, −2), and (3, −3). All lie on a line through the origin with slope −1.

Memory trick: (a, −a): a + (−a) = 0.