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A.F 3.1- Graph Functions A.F 3.3- Slope Per 3, 5: 11/22/10 Per 2, 4,6: 11/23/10

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AF 3.1- Graph Functions On the CAHSEE, you will be given a graph and must select the equation that best matches that graph

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Graph Equations y= x straight line (pointing right) y= -x straight line (pointing left) y= x 2 parabola (U shape, open up) y= -x 2 parabola (U shape, open down) y= x 3 cubic graph (snake shape, twisted) y= -x 3 cubic graph (snake shape, twisted)

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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.

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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 runx2-x1

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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

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

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Step 3: Plug the values where they go into the slope equation, and solve: Slope= y2-y1= 6-(-2)= 6+2 = 8 x2-x11-(-3) 1+3 4

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Answer: 2

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Slope cont. BIG NOTE: If you are asked to figure out the slope of a line, all you need to do is pick any two points on the line and plug their coordinates into the slope formula.

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Example: Given this graph: Find the slope

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

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

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

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Answer: 1/2

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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.

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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 48 Solve for x by cross multiplying

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Answer: Rise= 6

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Independent Practice 3.3 Part 2 Find the slope of a line that passes through the points 1.(3,1) and (1,4) 2.(3,5) and (4,7) 3.(-2,4) and (4,2) 4.(6,2) and (8,0) 5.(-2,-2) and (1,4) 6.(-5,3) and (7,-6) 7.(-3,2) and (1,4) 8.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? 9.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?

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