5.2 Defining Slope: 5.2 Defining Slope Brian Preston Algebra 1 2009-2010
Real World Application: How steep is this hiking trail? Real World Application
Lesson Objectives: Lesson Objectives 1) Find the slope of a line using two of its points. 2) Use the slope and any point on a line to write an equation of the line.
Review: Review 1) 10 – ( – 7) = 17 2) – 3 – 4 = – 7 3) – 5 + 9 = 4
Review: -1 -3 -2 -4 -5 -1 -3 -2 -4 -5 1 2 3 4 5 2 3 4 5 1 x x x x Review
Definition: Definition Slope – range of the Y-value range of the X-value Slope – m Slope – Rise Run
What is range?: What is range? range of the Y-value range of the X-value Slope – Range – Highest number minus the Lowest number
What does slope mean?: PRESTON P Rise Run Rise Run Rise Run Rise Run What does slope mean?
What does slope mean?: PRESTON P What does slope mean?
Real World Application: 4) Yara & Nidal are hiking up a hill. The run for Yara’s step is 32 inches, and the rise is 8 inches. The run for Nidal’s step is 36 inches, and the rise is 9 inches. Find the slope of the lines representing each hikers pathway up the hill. 32 32 of the Y-value of the X-value H-L H-L range range 8 9 36 Real World Application = 9 – 8 36 – 32 = 1 4 slope 8 9 36
Real World Application: 5) The coordinate plane below shows the position of a ladder resting against the side of a barn. Find the slope of the ladder. Real World Application
Real World Application: 5) The coordinate plane below shows the position of a ladder resting against the side of a barn. Find the slope of the ladder. Real World Application Rise Run = – 6 +2 – 3 =
Definition: Definition Slope – range of the Y-value range of the X-value Slope – m Slope – Rise Run y 2 – y 1 x 2 – x 1 Slope –
Example: 6) Find the slope of the line containing the points P(– 2,4) & Q(5,– 6). Example – 6 – 4 5 – – 2 = = y 2 – y 1 x 2 – x 1 – 10 7 – 2 4 – 6 5 ( ) ( ) ( ) ( ) (x 1 ,y 1 ) (x 2 ,y 2 ) 1 2
Example: 4 – – 6 ( ) 6) Find the slope of the line containing the points P(– 2,4) & Q(5,– 6). Example – 2 – 5 = = y 2 – y 1 x 2 – x 1 10 – 7 – 2 4 – 6 5 ( ) ( ) ( ) (x 2 ,y 2 ) (x 1 ,y 1 ) 2 1
Example: 7) Graph the line containing the point (– 2,3) and having slope m = – 4 +3 – 4 +3 -1 -3 -2 -4 -5 -1 -3 -2 -4 -5 1 2 3 4 5 2 3 4 5 1 Example (– 2,3) – 4 +3 Always make 3 points
Example: -1 -3 -2 -4 -5 -1 -3 -2 -4 -5 1 2 3 4 5 2 3 4 5 1 8) Graph the line containing the points (– 3,4) and (1,2). Example (– 3,4) (– 3,4) (1,2) (1,2)
Example: -1 -3 -2 -4 -5 -1 -3 -2 -4 -5 1 2 3 4 5 2 3 4 5 1 9) Use the Coordinates of point R and Point S to find the slope of the horizontal line shown below. Example 0 Rise Run = = Special line R S +5 ero 0 +5 0
Example: -1 -3 -2 -4 -5 -1 -3 -2 -4 -5 1 2 3 4 5 2 3 4 5 1 10) Use the Coordinates of Point J and Point K to find the slope of the vertical line shown below. Example – 5 0 Rise Run = = Special line J K – 5 u defined 0
Example: – 3 2 – 3 2 Rise = – 3 Run = 2 11) Find the slope. slope = – 3 2 Rise Run = Example
Example: x-int = 3 y-int = – 2 12) Find the slope. slope = 3 2 2 3 Rise Run = -1 -3 -2 -4 -5 -1 -3 -2 -4 -5 1 2 3 4 5 2 3 4 5 1 – 2 Example +2 +3 3
PowerPoint Presentation: 8 ÷ 0 = Definition Undefined means it doesn’t work, because we could put 0( nothing ) in the cup infinite times and still not reach 8 oz. undefined nothing nothing nothing nothing nothing nothing nothing nothing nothing
PowerPoint Presentation: u defined Key Points & Don’t Forget 1) A negative times a negative is a positive . – 3 – 5 = 15 – 2 0 2) Slope =
PowerPoint Presentation: pg. 231-232 #’s 11-19 odd, 20-42 even, 45, 47 The Assignment
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