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Equation of a Line. Special Cases. It’s What’s Going On!. Recall. y = m x + 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. Parallel Lines: Lesson. Parallel lines have the same slope or m value
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Equation of a Line Special Cases It’s What’s Going On!
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
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
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
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
Perpendicular Lines: Lesson • Perpendicular lines intersect each other at 90° angles • Perpendicular lines have slopes that are negative reciprocals of each other.
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
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
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
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
Horizontal Lines: Example • Remember, horizontal lines are parallel to the x-axis. • Example 1: y=2 • Example 2: y=4
Horizontal Lines: Application • Graph the following lines: • y=3 • y=1 • y=-2 • y=-3 Click the mouse to show answers
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.
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
Vertical Lines: Example • Remember, vertical lines are parallel to the y-axis. • Example 1: x=-2 • Example 2: x=1
Vertical Lines: Application • Graph the following lines: • x=2 • x=-3 • x=4 • x=1 Click the mouse to show answers
Horizontal & Vertical Reloaded • Graph the following lines: • x=2 • y=3 You are now a master of Horizontal and Vertical lines
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
Lessons Complete Horizontal and Vertical Lines Parallel and Perpendicular Lines