1. Company Name
7.1- Inverse Variation

2. Direct vs. Inverse Variation
Two variables x and y show Direct Variation when y=ax for some nonzero constant a. Ex: y = 5x, x = y/3, y = (1/2)x .
Two variables show Inverse Variation when they are related as follows:
The constant a is the constant of variation, and y is said to vary inversely with x.

3. Examples
Do x and y show direct variation, inverse variation, or neither?

4. Inverse Variation Relationship
When we talk about an inverse variation, we are talking about a relationship where
x increases, y decreases or
x decreases, y increases by a
CONSTANT FACTOR

5. Example
Table shows length x(inches) and width y(inches) of a rectangle. Area of every rectangle formed is 36 square inches. What is the equation to model the relationship between the length and width? x y 1 36 2 18 3 12 4 9 6
Follows form of , so it’s an inverse equation

6. Example(cont.d) Visual Representation

7. Examples of Inverse Variation:
What is the constant of variation of the table above?
Since , we can say k = xy. Therefore:
(-2)(-18)=k or k = 36
(72)(0.5)=k or k = 36
(4)(9)=k or k =36
xy = 36 or
y =
Note: k is constant

8. Using Inverse Variation to find Unknowns
Given that y varies inversely with x and y = -30 when x= -3, find y when x = 5.
2 step process
1. Find the constant variation.
k = xy or k = -3(-30)
k = 90
2. Use k = xy. Find the unknown (y).
90 = xy so 90= 5y
y= 18
Therefore:
when x = 5, y=18

9. Classifying Data (b) (a) Find the products xy and ratios y/x.
x and y show neither direct
nor inverse variation.
x and y show inverse variation.

10. Using Inverse Variation to Solve Word Problems
The time y that it takes a plane to reach a certain destination varies inversely as the average speed x of the plane. If it took a plane 3 hours to reach its destination when it traveled at an average speed of 150 mi/hr, what was the average speed of the plane if it took 4 hours to reach the same destination?

11. Using Inverse Variation to Solve Word Problems
Write the equation that relates the variables then solve.
The time y that it takes a plane to reach a certain destination varies inversely as the average speed x of the plane. If it took a plane 3 hours to reach its destination when it traveled at an average speed of 150 mi/hr, what was the average speed of the plane if it took 4 hours to reach the same destination?
t(time) varies inversely as s(speed) so
Time is the y variable
and
Speed is the x variable
K = xy
K = 150(3)
K = 450
The equation is 450 = xy
Substituting the new values:
450 = x(4)
x = 112.5
The average speed of the plane to reach the destination in 4 hours was mi/hr.

12. Graphs of Inverse Variation Equations