Parallel and Perpendicular Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Are the lines

y = -4x + 1

and

y = \frac{1}{4}x - 3

parallel, perpendicular, or neither?

1
Slopes: $m_1 = -4$ and $m_2 = \dfrac{1}{4}$ .
2
Check product: $m_1 \times m_2 = -4 \times \dfrac{1}{4} = -1$ . Since the product is $-1$ , the lines are perpendicular.

Answer

The lines are perpendicular.

Two lines are perpendicular when the product of their slopes is

-1

. Two lines are parallel when their slopes are equal. Here

(-4)(\frac{1}{4}) = -1

, confirming the lines meet at right angles.

About Parallel and Perpendicular

Parallel lines never intersect and have matching direction; perpendicular lines intersect at right angles.

Find the equation of the line through [formula] that is parallel to [formula].

Find the equation of the line through [formula] that is perpendicular to [formula].

Line [formula] passes through [formula] and [formula]. Find the equation of the line perpendicular t