Parallel and Perpendicular Lines Practice

Parallel Lines

• Parallel lines have the same slope and will never intersect.
• For point (2, -2) and line equation y = -x - 2, the parallel line's slope remains -1, resulting in the equation y = -x.
• For point (2, -1) and line equation y = -3/2x + 6, the parallel line has a slope of -3/2, leading to y = -3/2x + 2.
• A vertical line (x = -3) has a parallel line at x = 4, as all vertical lines are parallel to each other.

Perpendicular Lines

• Perpendicular lines have slopes that are negative reciprocals of each other.
• For point (-2, 3) and line y = 1/2x - 1, the slope is 1/2, so the perpendicular slope is -2, resulting in the equation y = -2x - 1.
• For point (5, 0) and line equation y + 1 = 2(x - 3), the slope of the given line is 2, leading to the perpendicular slope of -1/2, creating the equation y = -1/2x + 5/2.

Relationship of Graphs

• Two equations y = x + 11 and y = -x + 2 are perpendicular due to slopes of 1 and -1.
• The equations y = -2x + 3 and 2x + y = 7 represent parallel lines with a slope of -2.
• The equations y = 4x - 2 and -x + 4y = 0 are neither parallel nor perpendicular, with different slopes.

General Statements about Slopes

• The statement "Two lines with positive slopes are parallel" is categorized as sometimes true, as they could intersect at certain angles.
• The statement "Two lines with the same slope and different y-intercepts are perpendicular" is never true, as this configuration describes parallel lines instead.