Question

How should I know whether y=x+11 and y=-x+2 are perpendicular, parallel, or neither?

Answer 1

If their slopes are the same, they are parallel, If their slopes are negative inverses, then they are perpendicular. If the slopes are not the same or negative inverses, then they would be neither.

Answer 2

Both of these questions are in the slope-intercept form of y = mx + b. Here, m is the slope.

So, for the first, m = 1 (1 * x is just x) and the second is -1 (-1 * x is just - x).

These are indeed negative inverses, so the lines are perpendicular.