Tomorrow

1
Tomorrows TEST is worth 200 points and is the
last major grade on this report card!!!!
2
Unit 6 ReviewDirect Variation and Indirect
Variation

• Math 7 Unit 6
• Test Review

3
Inverse Variation Inverse Proportion

• There is no difference in the two. We simply call
  them by two different names

Direct Variation Direct Proportion

• There is no difference in the two. We simply call
  them by two different names

4
Inverse Proportion

• Remember
• As 1 variable increases, the other variable
  decreases when the constant is positive
• As 1 variable decreases, the other variable
  decreases when the constant is negative

5
The EQUATION for inverse variation can look
different at times

• The equation for inverse variation yk/x
• The equation may also be xyk
• The equation could be yxk as well
• THESE ARE ALL DIFFERENT WAYS OF WRITING THE SAME
  EQUATION!

6
Inverse Proportion in Word Problems

• In solving word problems for inverse proportion,
  we usually see the phrase is inversely
  proportional to or varies inversely as.

7
Graphing Inverse Proportion

• The graph of an inverse proportion is never a
  straight line!
• It is a smooth curve (hyperbola) that approaches
  the axis, but never touches or crosses them.

8
How does INVERSE VARIATION work?

• Bill is happy. He is thinking about that pizza
  he has ordered and will be delivered soon.
• One whole pizza just for him!!!

9
Now what?

• Oh look! His friend Gina is over.
• Well sharing with one person means he will get
  just half of the pizza!
• But he likes Gina.

10
And

• Bill looks out the window
• Robert is running to his house!
• Guess he heard about the pizza!
• Now Bill gets 1/3 of it!
• RATS!

11
Oh well

• Word is out on the street.
• Bill is getting pizza!
• Who invited Spike?
• What is happening to Bills pizza?
• What does that have to do with an inverse
  variation?

12
Lets look at what happened

• There was one pizza - 1
• Bill had one pizza - 1
• Gina shows up so Bill gets ½ of the pizza
• Robert runs to Bills house Bill gets 1/3 of
  the pizza
• Spike is headed to Bills Bill gets ¼ of the
  pizza!
• As each person enters, Bill gets less and less
  pizza.

13
And

• An algebraic form of this would be
• Y the pizza each one gets
• X the number of people
• K the constant (one pizza)
• Y K/X
• As the number of people increased, the amount of
  pizza each person got decreased.
• Thats easy!

14
Using what we did before

• If y varies inversely as x, and y 3 when x
  12, find x when y 4.
• First substitute your given information
• Second, find the value of the constant (K)
• Third, using the value of (K) that you just
  found substitute the new variable (y4) and
  solve for your new x (finding x)

15
Lets Review

• The formula for an inverse variation is
• What if we solved for k, what would it look like?

16
To solve for k

• You simply multiply each side by x.

17
Try this one

• If Y varies inversely as X, and y 6 when x
  12, find x when y9.

18
One more example

• If y varies inversely as x, if y 15 when x
  21, find x when y 27.

19
NOW Lets quickly review DIRECT
VARIATION/PROPORTION
20
Graphing DIRECT Variation

• DIRECT is always a linear equation that passes
  through the origin.

21
Direct Variation Equation

• The equation is ykx where k is the constant and
  can be positive or negative, but ? to zero.

22
Direct Variation/Proportion

• As one goes up, the other goes up (usually)
• As 1 variable increases, the other variable
  increases
• As 1 variable decreases, the other variable
  decreases when the constant is positive in
  quadrants 1 3
• Otherwise, as 1 variable increases, the other
  variable decreases when the constant is negative
  in quadrants
• 2 4.

23
Direct Variation Word Problems

• The direct proportion is another form of saying
• y varies directly with x.

24
Tomorrows TEST is worth 200 points and is the
last major grade on this report card!!!!
25
The End