Warm Up
1. A(n) ______________________________ “undoes” another
operation.
2. Find the constant of variation: 𝑦 = 7𝑥
3. Find the constant of variation: −4𝑦 = 12𝑥
4. Write a direct variation equation that contains the point (3, 9)
5. Write a direct variation equation that contains the point (−8, 4)
Lesson 64, Inverse Variation
Expressions and Equations
Inverse Variation
• Remember direct variation occurs between two variables if 𝑦 = 𝑘𝑥 and
𝑘 ≠ 0.
• ______________________ occurs when the product of two variables is a
constant _____________________
• We say that 𝑦 varies inversely as 𝑥
• ______________________ If (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) are solutions of an
inverse variation, then _______________
Example
Tell whether each relationship is an inverse variation. Explain.
a.
𝑦
6
=𝑥
b. 𝑥𝑦 = 5
Your turn
With a partner, Decide whether each relationship is an inverse
variation. Explain.
a. 3𝑥𝑦 = 9
b. 4𝑦 = 𝑥
Example
If 𝑦 varies inversely as 𝑥 and 𝑦 = 3 when 𝑥 = 12, find 𝑥 when 𝑦 = 9.
Your turn
With a partner, solve the following problem:
If 𝑦 varies inversely as 𝑥 and 𝑦 = 3.5 when 𝑥 = 20, find 𝑥 when 𝑦 =
10.
Example
Write and inverse variation relating 𝑥 to 𝑦 when 𝑦 = 8 and 𝑥 = 3. Then
graph the relationship.
Your turn
With a partner, write an inverse variation relating 𝑥 and 𝑦 when 𝑥 = 8
1
and 𝑦 = . Then graph the relationship.
2
Example
A truck driver is delivering goods from one state to another. Her speed
is inversely related to her travel time. If she is traveling at 55 miles per
hour, it will take her 13 hours to reach her destination. How long will it
take her if she travels at 65 miles per hour?
Your turn
Sierra found an inverse relationship between her hourly pay rate and
the number of hours she must work to earn a set amount. If she works
7 hours for $8 an hour, how long will she work at $10 an hour to earn
the same amount?