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 - PowerPoint PPT Presentation

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)

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### A.F 3.1- Graph FunctionsA.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= 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

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

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

• 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?