identify which lines are perpendicular
First, I am going to solve all of the lines that I can to slope intercept form:
1. y = 3x - 1 (solved to slope intercept form already)
2. y = 3
y = 0x + 3 (rewritten in slope intercept form)
3. x - 3y = 6
-3y = -x + 6 (subtract x from each side)
y = (1/3)x - 2 (dived each side by -3 to solve to slope intercept form
4. x = 6
0 = -x + 6
0y = -x + 6 (cannot solve to actual slope-intercept form)
Since 1 and 3 have the same sign on x (both are positive), they cannot be perpendicular to each other.
Line 2 is horizontal (slope is 0). Line 4 is vertical (the slope is undefined because you have to divide by 0 to find it).
Horizontal and vertical lines are perpendicular, so lines 2 and 4 are perpendicular.