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- The parallel line needs to have the same slope of 2. We can solve it by using the "point-slope" equation of a line: y − y1 = 2 (x − x1) And then put in the point (5,4): y − 4 = 2 (x − 5)
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Two lines are perpendicular when they meet at a right angle (90°). To find a perpendicular slope: When one line has a slope of m, a perpendicular line has a slope of −1 m. In other words the negative reciprocal.
- Slope
- −0.5
If the slopes are the same and the y -intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect. Their intersection forms a right or 90-degree angle. The two lines below are perpendicular.
Perpendicular to Parallel. Question: What is the difference between perpendicular and parallel? Answer: 90 degrees (a right angle) That's right, when we rotate a perpendicular line by 90° it becomes parallel (but not if it touches!)
Pairs of Angles. When parallel lines get crossed by another line (which is called a Transversal), you can see that many angles are the same, as in this example: These angles can be made into pairs of angles which have special names.
Perpendicular lines are lines in the same plane that intersect at right angles (90 degrees). Two nonvertical lines in the same plane, with slopes m1 and m2, are perpendicular if the product of their slopes is − 1: m1 ⋅ m2 = − 1. We can solve for m1 and obtain m1 = − 1 m2.
Parallel lines are lines that never intersect, and they form the same angle when they cross another line. Perpendicular lines intersect at a 90-degree angle, forming a square corner. We can identify these lines using angles and symbols in diagrams.
A pair of lines is perpendicular if the lines meet at \(90^\circ\) angle. Given two non-vertical lines in slope-intercept form \[ \begin{align} y &= m_1 x + b_1\\ y &= m_2 x + b_2, \end{align} \] the two lines are perpendicular if \(m_1 = - \frac{1}{m_2}\), that is, if the slopes are negative reciprocals of each other:
