Lines are parallel if their slopes are identical, and perpendicular if their slopes are negative reciprocals. Any other relationship between the lines would be neither parallel nor perpendicular. The first step in determining this relationship is to identify their slopes. To do that, let's make sure both lines are written in slope-intercept form.
Given Equation
Slope-intercept form
y=4x-2
y=4x-2
- x+4y=0
y=1/4x
Now, we can identify the slopes of the lines.
y&= 4 x-2 ⇒ m_1= 4
y&= 1/4 x ⇒ m_2= 1/4
Since the lines have different slopes, we can conclude that they are not parallel. To determine whether or not they are perpendicular, we calculate the product of the slopes. Any two slopes whose product equals - 1 are negative reciprocals, and therefore perpendicular.
