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Algebra ppt

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Algebra ppt

1. 1. Algebra 1- Slope
2. 2. Things that involve slope!
3. 3. <ul><li>Slope is the ratio between vertical rise and horizontal run between any 2 points on the same line. </li></ul><ul><li>Slope= vertical rise ÷ horizontal run </li></ul>The Slope Ratio
4. 4. <ul><li>Find the slope of a hill that has a vertical rise of 40ft and a horizontal run of 200 ft. </li></ul><ul><li>(Let m represent slope) </li></ul>Real Life Examples Vertical Rise = 40 ft Horizontal Run = 200 ft m= vertical/horizontal m= 40/200 = 1/5
5. 5. <ul><li>The slope m of a line that passes through points (x₁, y₁) and (x₂, y₂) is </li></ul>The Slope of a Line m= rise run = change in y change in x y₂-y₁ = x₂-x₁ <ul><li>Where (x₁, y₁) and (x₂, y₂) are any 2 points on the same line and x₁≠x₂. </li></ul>
6. 6. <ul><li>Let (x₁, y₁)= (1,0) and (x₂,y₂)=(3,4) </li></ul><ul><li>Find m. </li></ul>Positive Slope y₂-y₁ x₂-x₁ m= = 4-0 3-1 = 2 4 = 2 There is a positive slope of 2 therefore the line rises from left to right.
7. 7. Negative Slope Let (x₁, y₁)= (0,3) and (x₂,y₂)=(4,1) Find m. y₂-y₁ x₂-x₁ m= = 1-3 4-0 = 4 -2 = -1 There is a negative slope of -1/2 therefore the line falls from left to right. 2
8. 8. Zero Slope <ul><li>Let (x₁, y₁)= (1,2) and (x₂,y₂)=(4,2) </li></ul><ul><li>Find m. </li></ul>y₂-y₁ x₂-x₁ m= = 2-2 4-1 = 3 0 = 0 There is a zero slope therefore the line is horizontal. We can compare this to walking across the floor.
9. 9. Undefined Slope <ul><li>Let (x₁, y₁)= (3,-1) and (x₂,y₂)=(3,3) </li></ul><ul><li>Find m. </li></ul>y₂-y₁ x₂-x₁ m= = 3-⁻1 5-5 = 0 4 = Undefined! The slope is undefined because division by 0 is undefined and the expression 4/0 has no meaning. This line is vertical and we can compare it to walking up a wall, impossible.
10. 10. Summary: Slope of Lines Positive- rises left to right Negative- falls left to right Zero- horizontal Undefined- vertical
11. 11. <ul><li>y=mx+b where m and b are constants, then the graph of that equation is a line with slope m and y-intercept b. </li></ul><ul><li>The bigger the slope, the steeper the line. </li></ul><ul><li>Even of you choose completely different points on the same line, the slope will remain constant. </li></ul>Slope Intercept Form of a Line
12. 12. Example <ul><li>Find the slope and y-intercept of the line and then graph the line. </li></ul>3x + 5y −15 = 0 y= x+ 3 -3 5 Solve for y by subtracting 5y from both side and then divinding both sides by -5. slope y-intercept
13. 13. <ul><li>The top of the ladder is 12ft from the ground. The base of the ladder is 5ft from the wall. What is the slope of the ladder? </li></ul>Ladder rise 12 run 5 = 12ft 5ft
14. 14. Making Sense of Slope! A D C B E Choose different pairs of points on the line and find their slope. What do you notice? What conclusion can you draw?
15. 15. Making Sense of Slope! Anwsers mAB= mBC= mCD= mDE= 1 2 1 2 1 2 1 2 Now, based on the conclusion that the slope is ½ between each set of points, complete the sentence: No matter what pair of points you choose on a line, the ______ remains constant. *slope
16. 16. The Slope of the Road The slope of the road is the vertical rise divided by the horizontal run. If the vertical rise is 24 feet for a horizontal run of 1 mile, determine the slope of the road. *Hint- 1 mile=5280 feet 24ft 24ft 1 1mi 5280ft 220 = = *This means that for every 1ft that you move up, you also move 220ft forward.
17. 17. CREDITS <ul><li>Larson, Ron, Laurie Boswell, Timothy D. Kanold, and Lee Stiff. Algebra 1: Concepts and Skills . Teacher's ed. Evanston, IL: McDougal Littell, 2001. 229-233. Print. </li></ul><ul><li>Gustafson, R. David, and Peter D. Frisk. Beginning Algebra . Instructor's 3rd ed. Pacific Grove, CA: Brooks/Cole, 1992. 285-289. Print. </li></ul><ul><li>Håkan Dahlström, Six Flags Holland, 2/28/11 via Flickr, Creative Commons Attribution </li></ul><ul><li>Chad K., Hills Outside Silgo, 2/28/11 via Flickr, Creative Commons Attribution </li></ul><ul><li>Tony the Misfit, Snowboarding Along the East River, 2/28/11 via Flickr, Creative Commons Attribution </li></ul><ul><li>Pocius, Rooftops in Reykjavik, Iceland, 2/28/11 via Flickr, Creative Commons Attribution </li></ul><ul><li>Robert Couse-Baker, Up and Down the Ladder, 2/28/11 via Flickr, Creative Commons Attribution </li></ul><ul><li>Melissa, The Road Home, 2/28/11 via Flickr, Creative Commons Attribution </li></ul>