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3-3: Slopes of Lines. Expectation: You will calculate slopes of lines parallel and perpendicular to given lines. Slope. y. run. (x 1 ,y 1 ). rise. x. (x 2 ,y 2 ). y 2 -y 1. rise. =. Slope: m= . run. x 2 -x 1. 2-(-4). 6. 2. m=. =. =. 1. 3. -1-(-4). Slope. y. (-1,2). x.
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3-3: Slopes of Lines • Expectation: • You will calculate slopes of lines parallel and perpendicular to given lines. 3-3: Slopes of Lines
Slope y run (x1,y1) rise x (x2,y2) y2-y1 rise = Slope: m= run x2-x1 3-3: Slopes of Lines
2-(-4) 6 2 m= = = 1 3 -1-(-4) Slope y (-1,2) x (-3,-2) -2-(-4) (-4,-4) 2 m= = 1 -3-(-4) Points used does not matter!!! 3-3: Slopes of Lines
What is the slope of the line below? 3-3: Slopes of Lines
Calculate the slope of the line through: • (4,7) and (-5, 12) 3-3: Slopes of Lines
In the standard (x,y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,-8)? • -15 • -1 • -1/7 • 21/32 • 15 3.8: Analyzing Polygons
Horizontal and Vertical Lines • Draw the vertical line through (4,3) and (4,-6). • Calculate the slope of the line. • Is this true for all vertical lines? • Draw the horizontal line through (3,5) and (-3,5). • What is the slope of this line? • Is this true for all horizontal lines? 3-3: Slopes of Lines
Horizontal and Vertical Lines Slopes Theorem: • The slope of all vertical lines is ____________. • The slope of all horizontal lines is ___________. 3-3: Slopes of Lines
Slopes and Lines • Positive slope: line goes _____ from left to right • Negative slope: line goes ______ from left to right • Undefined slope: ____________ line • Slope of zero: _____________ line 3-3: Slopes of Lines
Parallel Lines and Slopes • Graph -3x + y = 4 and -3x + y = 1 on the same grid. • What appears to be true about the lines? • Calculate the slope of each line. • Make a conjecture about the slopes of parallel lines. 3-3: Slopes of Lines
Parallel Lines and Slopes Theorem: Two nonvertical lines are parallel iff their slopes are _______________. All vertical lines are ____________. 3-3: Slopes of Lines
Perpendicular Lines and Slopes • Carefully graph y = -2.5x – 2 and y = .4x + 4 on the same grid. • Measure the angle formed by the lines. • What appears to be true about the lines? • Calculate the slopes of the lines. • Make a conjecture about the slopes of perpendicular lines. 3-3: Slopes of Lines
Perpendicular Lines and Slopes Theorem Two nonvertical lines are perpendicular iff the product of their slopes is ____. Horizontal and vertical lines are ___________________. 3-3: Slopes of Lines
Determine whether the following lines are parallel, perpendicular or neither: -2x + y = 4 .5x + y = 8 3-3: Slopes of Lines
Calculate x so that the line through the points has slope of A(x,10) B(5,15) 3-3: Slopes of Lines
What is the slope of a line that is parallel to the line determined by the equation 5x – 4y = 8? • -4 • -5/4 • 5/4 • 2 • 4 3-3: Slopes of Lines
What is the slope of a line perpendicular to the line determined by the equation 7x + 4y = 11? • -4 • -7/4 • 11/4 • 4 • 4/7 3-3: Slopes of Lines
Assignment: pages 142-143,#17, 23, 27, 29, 39-43 (odds), 49 3-3: Slopes of Lines
