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A.F 3.1- Graph Functions A.F 3.3- SlopePowerPoint Presentation

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

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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

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)

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)

x2= 1

y2=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 3.3Part 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?

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