Notes on 8.1 Inverse Variation
Name __________________________
Direct Variation- in the form y=kx where k≠0.
Inverse Variation- in the form xy=k or y=𝑘/𝑥 𝑜𝑟 𝑥=𝑘/𝑦 where k≠0.
--------------------------------------------------------------------------------------------------------------------Direct Variation review (section 2.2)
Determine whether y varies directly with x? If so, state the constant of variation.
Example:
x
Y
1
2
3
6
4
8
--------------------------------------------------------------------------------------------------------------------Example: For each function, y varies directly with x; y=9 when x=-15 . What is y when x=21?
--------------------------------------------------------------------------------------------------------------------Indentifying direct variation and inverse variation
Example: Is the relationship between the variables a direct variation, and Inverse variation or neither?
Write function models for the direct and inverse variations.
X
Y
2
15
4
7.5
10
3
15
2
Example: Is the relation an inverse or direct variation, or neither?
X
Y
2
10
4
8
10
3
15
1.5
Determining an inverse variation
Suppose x and y vary inversely, and x=4 when y=12. What function models the inverse variation?
What is y when x=10?
--------------------------------------------------------------------------------------------------------------------Practice: Suppose x and y vary inversely, and x=8 when y=-7.
1) What is the function that models the inverse variation?
2) What is y when x=2?
--------------------------------------------------------------------------------------------------------------------Classwork/Homework