Sure! Here’s a quick overview of parallel and perpendicular lines:
Parallel Lines
- Definition: Parallel lines are two lines that run in the same direction but never intersect. They have the same slope.
- Equation: For lines in slope-intercept form (y = mx + b), if two lines have the same slope (m), they are parallel.
- Example: Line 1: y = 2x + 3 and Line 2: y = 2x - 4 are parallel.
Perpendicular Lines
- Definition: Perpendicular lines intersect at a right angle (90 degrees). The slope of one line is the negative reciprocal of the slope of the other.
- Equation: If one line has a slope of \( m_1 \) and another line has a slope of \( m_2 \), the lines are perpendicular if:
- \( m_1 \cdot m_2 = -1 \)
- Example: Line 1: y = 2x + 3 (slope = 2) and Line 2: y = -\frac{1}{2}x + 1 (slope = -\frac{1}{2}) are perpendicular since \( 2 \cdot -\frac{1}{2} = -1 \).
Quick Check Questions
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Determine if the following lines are parallel, perpendicular, or neither:
- Line 1: y = 3x + 1
- Line 2: y = 3x - 5
Answer: Parallel (same slope, m = 3).
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Determine if the following lines are parallel, perpendicular, or neither:
- Line 1: y = 1/3x + 2
- Line 2: y = -3x + 4
Answer: Perpendicular (1/3 and -3 are negative reciprocals).
-
Determine if the following lines are parallel, perpendicular, or neither:
- Line 1: y = -2x + 1
- Line 2: y = x + 5
Answer: Neither (slopes are -2 and 1, which are not the same and not negative reciprocals).
Feel free to ask if you have more specific examples or any other questions!
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