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A.F 3.1- Graph Functions A.F 3.3- Slope PowerPoint Presentation
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A.F 3.1- Graph Functions A.F 3.3- Slope

A.F 3.1- Graph Functions A.F 3.3- Slope

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A.F 3.1- Graph Functions A.F 3.3- Slope

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  1. A.F 3.1- Graph FunctionsA.F 3.3- Slope Per 3, 5: 11/21/11 Per 2, 4, 6: 11/22/11

  2. AF 3.1- Graph Functions • You will be given a graph and must select the equation that best matches that graph.

  3. Graph Equations • y= x straight line (pointing right) • y= -x straight line (pointing left) • y= x2parabola (U shape, open up) • y= -x2 parabola (U shape, open down) • y= x3 cubic graph (snake shape, twisted) • y= -x3 cubic graph (snake shape, twisted)

  4. AF 3.3- Slope • The slope is the number that tells how much a line rises (goes up) or falls (goes down) as it moves from left to right across the x-y plane.

  5. Slope Equation • With the slope equation, you can figure out the slope between any two ordered pairs (x1, y1) and (x2, y2). • Slope= rise= y2-y1 run x2-x1

  6. Example • Here’s how you would use the slope equation to find slope between the ordered pairs (-3, -2) and (1, 6): • Step 1: The first ordered pair is your (x1, y1), so: (x1, y1)= (-3, -2) x1= -3 y1= -2

  7. Step 2: • The second ordered pair is your (x2, y2), so: (x2, y2)= (1,6) x2= 1 y2=6

  8. Step 3: • Plug the values where they go into the slope equation, and solve: Slope= y2-y1= 6-(-2)= 6+2 = 8 x2-x1 1-(-3) 1+3 4 =2

  9. Slope cont. • BIG NOTE: If you are asked to figure out the slope of a line, • Pick any two points on the line and • plug their coordinates into the slope formula.

  10. Example: Given this graph: Find the slope

  11. Step 1: • Pick any two points. We’ll select (-2, -3) The ordered pair of any first point is your (x1, y1)

  12. Step 2 • The second ordered pair is your (x2, y2): We’ll select (4,0)

  13. Step 3: • Plug the values into the slope equation: Slope= y2-y1 x2-x1 Finish the problem and box your answer

  14. Answer: • 1/2

  15. Finding Rise or Run • Sometimes you will be asked to work backwards. You will be provided the slope, and you must find the rise or the run.

  16. Example • The slope of the line is 3/4. • The run is 8 What is the value of x (rise)? Slope= rise/run 3= x • 8 Solve for x by cross multiplying

  17. Answer: • Rise= 6

  18. Independent Practice 3.3 Find the slope of a line that passes through the points • (3,1) and (1,4) • (3,5) and (4,7) • (-2,4) and (4,2) • (6,2) and (8,0) • (-2,-2) and (1,4) • (-5,3) and (7,-6) • (-3,2) and (1,4) • Toni drew a graph of her hike on a coordinate plane. She passed 2 points on her way up. One was (-2,-2) and the other was (3,2). What is the slope of the hill? • Bill drew a graph of his ski run on a coordinate plane. On the way down he passed two trees. One tree was at point (4,-1) and the other was at point (-3,2). What is the slope of the hill?