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

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

Graph Equations y= x straight line (pointing right) y= -x straight line (pointing left) y= x2 parabola (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)

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.

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

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

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

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

Answer: 2

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.

Example: Given this graph: Find the slope

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

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

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

Answer: 1/2

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.

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

Answer: Rise= 6

Independent Practice 3.3 Part 2 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?