Cornell Notes
Topic/Objective:
Variation Functions
Algebra 2 Pre-AP
1st, 2nd, 6th, and 7th periods
October 11, 2013
Essential Question: What are variation functions? How do I use variation functions?
Questions:
Vocabulary
Direct Variation – A linear relationship between two variables, x and y, that can be written
in the form y = k x, where k is a nonzero constant.
*** A direct variation equation is a linear equation in the form y = m x + b, where b = 0
and the constant of variation k is the slope. Because b = 0, the graph of a direct variation
always passes through the origin.
y




x












Constant of Variation – The constant, k, in direct and inverse variation equations.
Inverse Variation – A relationship between two variables, x and y, that can be written in
𝑘
the form 𝑦 = 𝑥 , where k is a nonzero constant and x ≠ 0.
Notes
Taken from Algebra 2 textbook by Holt:
Many real world situations, from geometry and chemistry to engineering and agriculture,
can be modeled by variation functions.
Direct
Inverse
Variation
Variation
k is constant
𝑦 = 𝑘𝑥
As the value of one variable
increases, the value of the
other increases.
𝑦
𝑘=𝑥
Constant ratio
𝑘
𝑦=𝑥
As the value of one variable
increases, the value of the
other decreases.
𝑘 = 𝑦𝑥
Constant product
Graphs:
y
y








x








x













Direct Variation
Parent Function: Linear



Inverse Variation
Parent Function: Rational
Tell whether each statement is sometimes, always, or never true.
1. Direct Variation is a linear function. Always
2. A linear function is a direct variation. Sometimes
3. An inverse variation is a linear function. Never true
4. In a direct variation, x = 0 when y = 0. Always
5. The graph of an inverse variation passes through the origin. Never true
Examples
Given: y varies directly as x, and y = 14 when x = 3.5. What is the constant of variation?
𝑦 = 𝑘𝑥
14 = 𝑘(3.5)
14 𝑘(3.5)
=
3.5
3.5
4=𝑘
Given: y varies inversely as x, and y = 3 when x = 8. What is the constant of variation?
𝑘
𝑦=
𝑥
𝑘
3=
8
𝑘
8∗3= ∗8
8
24 = 𝑘
The wavelength λ of a wave of a certain frequency varies directly as the velocity ν of the
wave. If λ = 60ft when ν = 15ft/s, then find λ when ν = 3ft/s.
𝜆 = 𝑘𝜐
SO,
𝜆 = 𝑘𝜐
60 = 𝑘(15)
λ = 4*3
60
𝑘(15)
= 15
λ = 12 ft.
15
4=𝑘