Perpendicular lines
By definition, perpendicular lines are two lines that cross at a 90° angle. If two lines are perpendicular, their slopes are negative inverses of one another. Let's say that line A is perpendicular to line B, and A's slope is 2. Then, B's slope would be -1/2.
The problem is asking us to show that lines x - 3y = 6 and 4y = 12x are perpendicular. Well, to make the decision, we first need to write both of these in slope-intercept form.
slope-intercept form
The format of slope-intercept equations is y = mx + b (m = slope and b = y-intercept).
So we need to write x - 3y = 6 in y = mx + b.
-3y = 6 - x
-3y = -x + 6
3y = -x - 6
y = x/3 - 6/3
y = x/3 - 2
Now, the second equation:
4y = 12x
y = 3
The lines aren't perpendicular since their slopes are not negative inverses of one another.