Slopes of Parallel and Perpendicular Lines
Give at least two real world examples of parallel and perpendicular lines.
Definition: Parallel lines are lines that never intersect and are always the same distance
apart.
Explore Parallel Lines
1. Graph each of the following equations on the same Cartesian coordinate system.
a. y = -½x + 1
b. y = -½x – 3
c. y = y = -½x + 5
√
2. What relationship appears to exist among the graphs of the three equations?
3. What relationship exists among the equations?
√
√
4. Complete the following conjecture (to conclude or form opinions based on evidence).
Lines that are parallel have _________ slopes.
Definition: Two nonvertical lines are parallel if they have the same slope and different yintercepts. All vertical lines are parallel.
Write the equation of a line that is parallel to the graph of y = 2/3 x – 4 and contains the point
(-6, 1).
Definition: Perpendicular lines are lines that intersect to form right angles. Recall that right
angles are angles that measure 90°.
Explore Perpendicular Lines
1. Graph both of the following equations on the same Cartesian coordinate system.
a. y = -2x + 4
b. y = ½ x – 2
√
2. What relationship appears to exist among the graphs of the equations?
√
3. Graph both of the following equations on the same Cartesian coordinate system.
a. y = ¾ x – 1
b. y = -4/3 x + 2
√
4. What relationship appears to exist among the graphs of the equations?
√
5. Examine the pairs of equations in Steps 1 and 3. What relationship exists among each
pair of equations?
√
The slopes of lines that are
perpendicular are _____________ _____________.
6. Complete the conjecture:
Definition: Two lines are perpendicular if their slopes are negative reciprocals. A vertical
and a horizontal line are perpendicular.