1. Warm-up b) a) Solve the following equation.
Solve the sets of equations. a) b)

2. Inverse
Objective: We can set up inverse relationships.
VARIATION

3. Quick Review
When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.

4. The general equation for DIRECT VARIATION is
k is called the constant of variation.
We will do an example together.

5. (a) Find the constant of variation
If y varies directly as x, and y=24 and x=3 find: (a) the constant of variation
(b) Find y when x=2
(a) Find the constant of variation
Write the general equation
Substitute

6. (b) Find y when x=2
First we find the constant of variation, which was k=8
Now we substitute into y=kx.

7. Another method of solving direct variation problems is to use proportions.
Therefore...

8. So lets look at a problem that can by solved by either of these two methods.

9. What does the graph y=kx look like?
A straight line with a y-intercept of 0.

10. Looking at the graph, what is the slope of the line?
Answer: 3
Looking at the equation, what is the constant of variation?
Answer: 3
The constant of variation and the slope are the same!!!!

11. Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. There is not necessarily a constant rate.

12. Inverse Variation
y varies inversely as x if
such that xy=k or
Just as with direct variation, a proportion can be set up solve problems of indirect variation.

13. A general form of the proportion
Lets do an example that can be solved by using the equation and the proportion.

14. Find y when x=15, if y varies inversely as x and x=10 when y=12
Solve by equation:

15. Solve by proportion:

16. Solve this problem using either method.
Find x when y=27, if y varies inversely as x and x=9 when y=45.
Answer: 15

17. Lets apply what we have learned.
The pressure P of a compressed gas is inversely proportional to its volume V according to Boyle’s Law. A pressure of 40 pounds per square inch is created by 600 cubic inches of a certain gas. Find the pressure when the gas is compressed to 200 cubic inches.

18. Step #1: Set up a proportion.

19. Now try this one on your own.
A pressure of 20 pounds per inch squared is exerted by 400 inches cubed of a certain gas. Use Boyle’s Law to find the pressure of the gas when it is compressed to a volume of 100 inches cubed.

20. What does the graph of xy=k look like? Let k=5 and graph.

21. This is a graph of a hyperbola.
Notice: That in the graph, as the x values increase the y values decrease.
also
As the x values decrease the y values increase.

22. Partner Work

23. Swap Meet: Unit 2 & 4
Write everything you know about the following topics on the LEFT SIDE
Unit 4
Surface Area
Volume
Density
Population Density
Distance and Midpoint Formula
Equation of a Circle
on the RIGHT SIDE
Unit 2
Midsegments
Triangle Congruence Theorems
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Vertical, supplementary, complementary angles
Bisectors
Angles in a triangle
Isosceles and Equilateral Triangles

24. Swap Meet
Flip your card over so it is facing down (you cannot see the writing)
Walk around and exchange cards until the music stops
Now, read cards and star something you did not know before reading it
If you see an error, CORRECT IT!
Now, exchange cards but READ EVERY CARD YOU GET before passing it along
Last step, jot down one topic you still need practice with

25. Exit Ticket Quick write:
In your own words explain the difference between direct variation and inverse variation.
Write the equation for the circle with these parameters:
Find the length of the midsegment.