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Understanding Line Equations: Parallel, Perpendicular, Horizontal, and Vertical

Explore the equations of lines and their special cases such as parallel and perpendicular lines, as well as horizontal and vertical lines. Learn how to identify relationships between various lines and apply the concepts to graphing exercises. Master the concepts through examples and applications, and access helpful web resources for further learning.

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Understanding Line Equations: Parallel, Perpendicular, Horizontal, and Vertical

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  1. Equation of a Line Special Cases It’s What’s Going On!

  2. Recall • y = mx + b is the equation of a line • m is the value of the slope of a line (rise over run) • b is the y-intercept m = 1 __ b = 0 2

  3. Parallel Lines: Lesson • Parallel lines have the same slope or m value • Parallel lines are always the same distance apart • Parallel lines move in the same direction and never meet Same distance throughout

  4. Parallel Lines: Application • Graph the following lines: • y=4x-3 and y=4x-1 • What is the relationship between these lines? • Graph two more lines with this relationship y = 4x-1 y = 4x-3

  5. Parallel Lines: Application • Graph the line y=2x+1 • Graph a line parallel to this line with a y-intercept at 4 y-intercept y = 2x+1

  6. Perpendicular Lines: Lesson • Perpendicular lines intersect each other at 90° angles • Perpendicular lines have slopes that are negative reciprocals of each other.

  7. Perpendicular Lines: Application • Graph the following lines: • y=1x+1 and y=-2x+1 • What is the relationship between these lines? • Graph 2 more lines with this relationship. _ 2 y = 1x + 1 __ y = -2x + 1 2

  8. Perpendicular Lines: Application • Graph the line y=3x + 2 • Graph a line perpendicular to this line with a y-intercept at 3. _ 4 y = 3x + 2 _ 4

  9. Horizontal Lines Introduction • Lines that are horizontal have a slope of zero. They have "run", but no "rise". The rise/run formula for slope always yields zero since

  10. Horizontal Lines: Lesson • Horizontal lines have no x-intercept • They are parallel to the x-axis • If (0,1) is y-intercept of a horizontal line, then the equation of the line is y=1 • Have a undefined slope

  11. Horizontal Lines: Example • Remember, horizontal lines are parallel to the x-axis. • Example 1: y=2 • Example 2: y=4

  12. Horizontal Lines: Application • Graph the following lines: • y=3 • y=1 • y=-2 • y=-3 Click the mouse to show answers

  13. Vertical Lines Introduction • Lines that are vertical have no slope (it does not exist).  They have "rise", but no "run".  The rise/run formula for slope always has a zero denominator and is undefined.

  14. Vertical Lines: Lesson • Vertical lines have no y-intercept • They are parallel to the y-axis • If (1,0) is x-intercept of a vertical line, then the equation of the line is x=1 • Have a undefined slope

  15. Vertical Lines: Example • Remember, vertical lines are parallel to the y-axis. • Example 1: x=-2 • Example 2: x=1

  16. Vertical Lines: Application • Graph the following lines: • x=2 • x=-3 • x=4 • x=1 Click the mouse to show answers

  17. Horizontal & Vertical Reloaded • Graph the following lines: • x=2 • y=3 You are now a master of Horizontal and Vertical lines

  18. Web-sites to visit: • http://www.math.com/school/subject3/lessons/S3U1L3GL.html • http://www.sci.wsu.edu/~kentler/Fall97_101/nojs/Chapter3/section2.html • http://regentsprep.org/Regents/math/line-eq/EqLines.htm • http://www.hoxie.org/math/algebra/stline1.htm

  19. Lessons Complete Horizontal and Vertical Lines Parallel and Perpendicular Lines

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