Question

Which statement is true about the graphs of the two lines y = x + 2 and y = x ?

The lines are perpendicular to each other because and are opposite reciprocals of each other.
The lines are perpendicular to each other because 2 and are opposite reciprocals of each other.
The lines are neither parallel nor perpendicular to each other because and are not opposite reciprocals of each other.
The lines are neither parallel nor perpendicular to each other because 2 and are not opposite reciprocals of each other.

Answer 1

Neither of the given statements is correct. Both lines have slope 1 (y = x + 2 has m = 1 and y = x has m = 1), so they are parallel (same slope) and distinct (different y‑intercepts). They are not perpendicular, since perpendicular slopes would be opposite reciprocals (product −1), but 1·1 ≠ −1.