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#### Presentation Transcript

**1. ** Graphs by Michael Okito December 2004

**2. **What you will learn In this presentation, I will be teaching you how to graph linear equations.
These linear equations will always be variations such as direct variations, inverse variations, inverse squares and etc.

**3. **Index Lesson 1: the graph of y=kx
Quiz #1
Lesson 2: the graph of y=kx2
Quiz #2
Lesson 3: the graph of y=k/x and y=k/x2
Quiz #3

**4. **Lesson 1: the graph of y=kx The equation y=kx is a direct variation. Its graph is always a straight line that usually goes through the origin (the 0,0 point).
In the equation y=kx, y is the dependent variable or the variable that lies on the y-axis. X is the independent variable that lies on the x-axis. The k represents the slope or the rate of change.
To graph a direct variation, you first have to plug in different values for x in the formula then find the value of y. Finally all you have left to do is to plot the points in the graph and connect them.

**5. **…Lesson 1: Continued. 8 y=2x
6 y=x
4
2 y=1/4x
-8 -6 -4 -2 0 2 4 6 8
-2
-4
-6 y=-x
-8 y=-2x

**6. **Quiz #1 a
b
c
Which line follows the equation y=3x?
1- a)
2- b)
3- c)

**7. **CONGRATULATIONS!!!! YOU CAN NOW MOVE ON TO THE NEXT LESSON!!!

**8. **SORRY!! Go Back and Reread the Lesson!!!!!!!!

**9. **Lesson 2: the graph of y=kx2 The graph of y=kx2 is quite similar to the graph of y=kx. The only difference between their graphs is that the graph of y=kx2 has a parabola instead of a straight line.
The graph of y=kx2 is a parabola because different pairs of points have different slopes.
To graph an equation of this form, you do exactly the same thing as what you did with the graph of y=kx.

**10. **…Lesson 2: Continued. Example: The distance needed to stop a bike after applying the brakes varies directly with the square of the bike’s speed. The formula d=1/8s2 describes the relation between braking distance and speed for a certain bike.
The table below gives some solutions to this equation.
Braking distance
(ft)
speed (mph)

**11. **Quiz #2 The graph of y=kx2 is a
Symmetry
Line
Slope
Parabola
cube

**12. **CONGRATULATIONS!!!! YOU CAN NOW MOVE ON TO THE NEXT LESSON!!!

**13. **SORRY!! Go Back and Reread the Lesson!!!!!!!!

**14. **Lesson 3: the graph of y=k/x and y=k/x2 Example 1: Draw the graphs of y=16/x and y=-16/x for x=0
20 20
10 10
-20 -10 0 10 20 -20 -10 0 10 20
-10 -10
-20 -20

**15. **…Lesson 3: Continued. The type of curve in the previous example is called a hyperbola. It has two separate parts called branches. The branches of a hyperbola are always located on quadrants opposite to each other.
The graphs below have two branches too but they only have branches on quadrants that are next to each other. These graphs are inverse square square graphs.
Example 2: Graph y=16/x2 and y=-16/x2

**16. **Quiz #3 Refer to the following equations:
a) y=kx b) y=kx2 c) y=k/x d) y=k/x2
The graph of which equation is a hyperbola?
1- a)
2- b)
3- c)
4-d)

**17. **SORRY!! Go Back and Reread the Lesson!!!!!!!!

**18. **CONGRATULATIONS!!!! Now you’re a master at graphs