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# Int Math 2 Section 6-1 1011

## by Jimbo Lamb, Math Teacher and Technology Coach at Annville-Cleona Secondary School on Feb 24, 2011

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Slope of a Line

Slope of a Line

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## Int Math 2 Section 6-1 1011Presentation Transcript

• Section 6-2 Slope of a Line
• Essential QuestionsHow do you ﬁnd the slope of a line?How do you identify horizontal andvertical lines?Where you’ll see it: Business, science, transportation
• Vocabulary1. Slope:
• Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change
• Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again.
• Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again.1. Slope:
• Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again.1. Slope: How steep a line is, measured in “rise over run”
• Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again.1. Slope: How steep a line is, measured in “rise over run” Formula:
• Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again.1. Slope: How steep a line is, measured in “rise over run” Formula: y 2 − y1 m= , for points ( x 1 , y 1 ) and ( x 2 , y 2 ) x 2 − x1
• MATH CALISTHENICS!
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line.C = (−4,0)D = (4, 4)
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line.C = (−4,0) CD = (4, 4)
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line. DC = (−4,0) CD = (4, 4)
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line. DC = (−4,0) CD = (4, 4)
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line. y 2 − y1 D m= x 2 − x1C = (−4,0) CD = (4, 4)
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line. y 2 − y1 D m= x 2 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4)
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line. y 2 − y1 D m= x 2 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4) 4 = 8
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line. y 2 − y1 D m= x 2 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4) 4 1 = = 8 2
• Example 1 Graph the line the goes through the given points, then ﬁnd the slope of the line. y 2 − y1 D m= x 2 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4) 4 1 = = 8 2 Here, the slope tells us “Up 1, Right 2”
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4)
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3 −9
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3 −9 0 = −6
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3 −9 0 = =0 −6
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3 −9 0 = =0 −6 Horizontal
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) = 3 −9 0 = =0 −6 Horizontal
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 1 2 = = 3 −9 3 −3 0 = =0 −6 Horizontal
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 1 2 = = 3 −9 3 −3 0 −1 6 = =0 = −6 0 Horizontal
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 1 2 = = 3 −9 3 −3 0 −1 6 = =0 = Undeﬁned −6 0 Horizontal
• Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 1 2 = = 3 −9 3 −3 0 −1 6 = =0 = Undeﬁned −6 0 Horizontal Vertical
• Horizontal vs. Vertical
• Horizontal vs. Vertical Horizontal lines have slopes of
• Horizontal vs. Vertical Horizontal lines have slopes of zero
• Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”)
• Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is
• Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is undeﬁned
• Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is undeﬁned (It’s neither uphill, downhill, or level)
• Example 3Graph the line that passes through P = (-1, 1) and has a slope of -2.
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2−2 = 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1Down 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
• Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4)
• Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) y 2 − y1 m (AB ) = x 2 − x1
• Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) y 2 − y 1 2 − (−1 ) m (AB ) = = x 2 − x1 2−0
• Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) y 2 − y 1 2 − (−1 ) 3 m (AB ) = = = x 2 − x1 2−0 2
• Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) y 2 − y 1 2 − (−1 ) 3 m (AB ) = = = x 2 − x1 2−0 2 y 2 − y1 m (CD ) = x 2 − x1
• Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) y 2 − y 1 2 − (−1 ) 3 m (AB ) = = = x 2 − x1 2−0 2 y 2 − y1 4 −1 m (CD ) = = x 2 − x 1 −1 − (−3)
• Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) y 2 − y 1 2 − (−1 ) 3 m (AB ) = = = x 2 − x1 2−0 2 y 2 − y1 4 −1 3 m (CD ) = = = x 2 − x 1 −1 − (−3) 2
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4)
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) A
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) B A
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) B C A
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) D B C A
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) D B C A
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) D B C A
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) D B The lines are parallel. C A
• Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) D B The lines are parallel. C A They have the same slope.
• Problem Set
• Problem Set p. 250 #1-35 odd“The power of imagination makes us inﬁnite.” - John Muir