Warmup What is the negative reciprocal of 1
- Slides: 16
Warm-up What is the negative reciprocal of… 1. ½ 2. 4 3. -3/2 4. -8
Slopes of Parallel & Perpendicular Lines
Slope: the ratio of vertical change to the horizontal change Notation: m
Example run rise
FOUR POSSIBLE SLOPES
Examples: Find the slope of the line through the given points. a. (-4, 7) and (3, 7) b. (1, -4) and (2, 5) c. (3, -1) and (3, 2) d. (-2, 5) and (1, -1)
Parallel Postulate There is exactly one line through P parallel to.
Perpendicular Postulate There is exactly one line through P perpendicular to.
Investigation Time!
Slopes of Parallel Lines Two lines are parallel if and only if they have equal slopes.
Slopes of Perpendicular Lines Two lines are perpendicular if and only if the product of their slopes is -1 (reciprocals and opposite signs).
Example: Finding Perpendicular Slopes
Examples Any line parallel to a line with slope has slope _____. Any line perpendicular to a line with slope has slope ___. 0 Any line parallel to a line with slope 0 has slope _____. Any line perpendicular to a line with undefined slope has slope______. Zero Slope 13
Examples Line 1: through (1, 2) and (4, -3) Line 2: through (-4, 3) and (-1, -2) Line 1: through (-2, 2) and (0, -1) Line 2: through (-4, -1) and (2, 3) Line 1: through (1, 5) and (3, -2) Line 2: through (-3, -2) and (4, 0)
Examples Are these parallel? Are these perpendicular?
Find the slope of each line by counting (change in y to change in x). Determine if the lines are parallel, perpendicular, or neither.
