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3.4 Slopes of Lines                                                                   September 27, 2011




                                 BELLWORK                                                    #3­4
     1. Find the value of x that make p // q.                                                    a
                 #1
                           (2x + 43)             (3x)
                  p
       x = 43                                                                                    b
                                         q
                                                        3. Can you prove a // b?           yes
     2. Which lines are parallel? 
            E                                F          4. If so, what theorem would you use?
                 95                 80
                                                                Alt. Interior < Converse

            85                100                       5. Are you ready for the 3.1­3.3 Quiz 
        D                           G
                                                        on Wednesday?         I hope so!
                EF // DG




HW pg. 175 #3­9 odd, 13­29 odd                                                                             1
3.4 Slopes of Lines                                                 September 27, 2011



                         3.4 Find and Use Slopes of Lines
     Slope: ratio of vertical change (rise) to horizontal change (run)
     between any 2 points.
                                                                 run (x2 - x1)

     Slope = rise change in y       y -y
             run
                 = change in x   = x22 - x11    rise (y2 - y1)




     Negative Slope: falls from left to right

     Positive Slope: rises from left to right

     Zero Slope: horizontal line

     Undefined Slope: vertical line




HW pg. 175 #3­9 odd, 13­29 odd                                                           2
3.4 Slopes of Lines                                                   September 27, 2011

           Comparing Slopes: When 2 lines intersect, the steeper line has
           the slope with greater absolute value.

           Postulate 17: Slopes of Parallel Lines
                       2 lines are // iff they have the same slope.
           m1 = m2

           Postulate 18: Slopes of Perpendicular Lines
                        2 lines are  iff the product of their slopes is -1.
           m1 * m2 = -1




HW pg. 175 #3­9 odd, 13­29 odd                                                             3
3.4 Slopes of Lines                                      September 27, 2011




      With your horizontal partner, complete #3 in guided practice.




HW pg. 175 #3­9 odd, 13­29 odd                                                4
3.4 Slopes of Lines              September 27, 2011




HW pg. 175 #3­9 odd, 13­29 odd                        5
3.4 Slopes of Lines              September 27, 2011




HW pg. 175 #3­9 odd, 13­29 odd                        6
3.4 Slopes of Lines                                September 27, 2011




     With your horizontal partner,
     complete problems 4 & 5 in guided practice.




HW pg. 175 #3­9 odd, 13­29 odd                                          7
3.4 Slopes of Lines              September 27, 2011




     HW pg. 175 #3-9 odd, 13-29 odd




HW pg. 175 #3­9 odd, 13­29 odd                        8

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3.4 notes

  • 1. 3.4 Slopes of Lines September 27, 2011 BELLWORK #3­4 1. Find the value of x that make p // q. a #1 (2x + 43) (3x) p x = 43 b q 3. Can you prove a // b? yes 2. Which lines are parallel?  E F 4. If so, what theorem would you use? 95 80 Alt. Interior < Converse 85 100 5. Are you ready for the 3.1­3.3 Quiz  D G on Wednesday? I hope so! EF // DG HW pg. 175 #3­9 odd, 13­29 odd 1
  • 2. 3.4 Slopes of Lines September 27, 2011 3.4 Find and Use Slopes of Lines Slope: ratio of vertical change (rise) to horizontal change (run) between any 2 points. run (x2 - x1) Slope = rise change in y y -y run = change in x = x22 - x11 rise (y2 - y1) Negative Slope: falls from left to right Positive Slope: rises from left to right Zero Slope: horizontal line Undefined Slope: vertical line HW pg. 175 #3­9 odd, 13­29 odd 2
  • 3. 3.4 Slopes of Lines September 27, 2011 Comparing Slopes: When 2 lines intersect, the steeper line has the slope with greater absolute value. Postulate 17: Slopes of Parallel Lines 2 lines are // iff they have the same slope. m1 = m2 Postulate 18: Slopes of Perpendicular Lines 2 lines are iff the product of their slopes is -1. m1 * m2 = -1 HW pg. 175 #3­9 odd, 13­29 odd 3
  • 4. 3.4 Slopes of Lines September 27, 2011 With your horizontal partner, complete #3 in guided practice. HW pg. 175 #3­9 odd, 13­29 odd 4
  • 5. 3.4 Slopes of Lines September 27, 2011 HW pg. 175 #3­9 odd, 13­29 odd 5
  • 6. 3.4 Slopes of Lines September 27, 2011 HW pg. 175 #3­9 odd, 13­29 odd 6
  • 7. 3.4 Slopes of Lines September 27, 2011 With your horizontal partner, complete problems 4 & 5 in guided practice. HW pg. 175 #3­9 odd, 13­29 odd 7
  • 8. 3.4 Slopes of Lines September 27, 2011 HW pg. 175 #3-9 odd, 13-29 odd HW pg. 175 #3­9 odd, 13­29 odd 8