2. 12/23/2015 3-3: Slopes of Lines 1 Expectation: You will calculate slopes of lines parallel and perpendicular to given lines.

3. 12/23/2015 3-3: Slopes of Lines 2 Slope x y (x 1,y 1 ) (x 2,y 2 ) rise run Slope: m= rise run = y 2 -y 1 x 2 -x 1

4. 12/23/2015 3-3: Slopes of Lines 3 Slope x y (-4,-4) (-3,-2) (-1,2) m= 2-(-4) -1-(-4) = 6 3 = 2 1 m= -2-(-4) -3-(-4) = 2 1 Points used does not matter!!!

5. 12/23/2015 3-3: Slopes of Lines 4 What is the slope of the line below?

6. 12/23/2015 3-3: Slopes of Lines 5 Calculate the slope of the line through: (4,7) and (-5, 12)

7. 12/23/2015 3.8: Analyzing Polygons In the standard (x,y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,-8)? A)-15 B)-1 C) -1 / 7 D) 21 / 32 E)15

8. 12/23/2015 3-3: Slopes of Lines 7 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?

9. 12/23/2015 3-3: Slopes of Lines 8

10. 12/23/2015 3-3: Slopes of Lines 9 Horizontal and Vertical Lines Slopes Theorem: The slope of all vertical lines is ____________. The slope of all horizontal lines is ___________.

11. 12/23/2015 3-3: Slopes of Lines 10 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

12. 12/23/2015 3-3: Slopes of Lines 11 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.

13. 12/23/2015 3-3: Slopes of Lines 12 Parallel Lines and Slopes Theorem: Two nonvertical lines are parallel iff their slopes are _______________. All vertical lines are ____________.

14. 12/23/2015 3-3: Slopes of Lines 13 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.

15. 12/23/2015 3-3: Slopes of Lines 14

16. 12/23/2015 3-3: Slopes of Lines 15 Perpendicular Lines and Slopes Theorem Two nonvertical lines are perpendicular iff the product of their slopes is ____. Horizontal and vertical lines are ___________________.

18. 12/23/2015 3-3: Slopes of Lines 17 Determine whether the following lines are parallel, perpendicular or neither: -2x + y = 4.5x + y = 8

20. 12/23/2015 3-3: Slopes of Lines 19 Calculate x so that the line through the points has slope of A(x,10) B(5,15)

21. What is the slope of a line that is parallel to the line determined by the equation 5x – 4y = 8? A)-4 B) -5 / 4 C) 5 / 4 D)2 E)4 12/23/2015 3-3: Slopes of Lines 20

22. What is the slope of a line perpendicular to the line determined by the equation 7x + 4y = 11? A)-4 B) -7 / 4 C) 11 / 4 D)4 E) 4 / 7 12/23/2015 3-3: Slopes of Lines 21

27. 12/23/20153-3: Slopes of Lines 26 Assignment: pages 142-143, #17, 23, 27, 29, 39-43 (odds), 49