Notes: Variations
SOL A1.8
Name_________________________________
Date__________________________
Investigation: Direct Variation
As you watch a movie, 24 individual pictures, or frames, flash on the screen each second. Here are
three ways you can model the relationship between the number of frames f(s) and the number of
seconds s.
Table
s
number of
seconds
1
2
3
4
5
Graph
Function Rule
𝑓(𝑠) = 24𝑠
f(s)
number of
frames
24
48
72
96
120
1) As the number of seconds doubles, what happens to the number of frames? _____________________
2) Find the ratio
Pair
Ratio
number of frames
for each pair in the table
number of seconds
1st
2nd
3rd
4th
5th
frames
seconds
3) For every increase of 1 second on the horizontal axis of the graph, what is the increase on the
vertical axis? _____________________________________________________________________________
4) What do you notice about your answers to Questions 2 and 3 and the coefficient of s in the function
rule? _____________________________________________________________________________________
__________________________________________________________________________________________
5) What number of frames correspond to s = 0? ________________________________________________
6) What is the ordered pair on the graph for the seconds and number of frames when s = 0? _________
__________________________________________________________________________________________
Notes: Variations
SOL A1.8
A direct variation is a function _______________________________________________________________
__________________________________________________________________________________________
Look back at the 3 examples in the investigation on page 1.
A direct variation will always form a graph that will be __________________________________________
__________________________________________________________________________________________
Sketch 3 graphs that represent direct variations.
The constant of proportionality in direct variation is represented by the ___________________________
__________________________________________________________________________________________
y = kx
To see if direct variation exists in a table:
1. Verify ______________________________________________________________________________
2. ____________________________________________________________________________________
State whether the following are direct variations. If so, write the equation for the function and state
what the constant of variation is.
The constant variation is ____________, ____________, ____________, ____________
1st pair
2nd pair
Are all ratios the same? __________________
The direct variation ____________________.
3rd pair
4th pair
Notes: Variations
SOL A1.8
The constant variation is ____________, ____________, ____________, ____________
1st pair
2nd pair
3rd pair
4th pair
Are all ratios the same? __________________
The direct variation ______________________.
X
-3
6
1
Y
2.25
-4.5
-0.75
The constant variation is ____________, ____________, ____________
1st pair
2nd pair
3rd pair
Are all ratios the same? __________________
The direct variation is ____________________.
McDonalds pay is $123 for 20 hours. Karen was paid $190.65 for working 31 hours.
this represents a direct variation.
_____________
(Input)
_____________
(Output)
State whether
Ratio
Does direct variation exist?____________________. If so, what is the equation? ____________________
On Saturday, a dishwasher used 65 gallons of water to wash 5 loads of dishes. On Sunday another
dishwasher used 156 gallons to wash 9 loads. State whether this represents a direct variation.
_____________
(Input)
_____________
(Output)
Ratio
Does direct variation exist? ____________________. If so, what is the equation? ___________________
Notes: Variations
SOL A1.8
Find the constant of variation and write an equation each situation.
1) The number of gallons of gas used varies directly with the number of miles traveled. A car gets
24 miles to the gallon.
k = ___________________________
Equations: _____________________________
2) The amount of blood in a person’s body varies directly with body weight. A person who weighs
160 pounds has about 5 quart of blood.
k = ___________________________
Equations: _____________________________
Each point on the graphs below is on a line from an equation of a direct variation. Plot 3 other points
on the line.
Inverse Variations
An inverse variation is a function ____________________________________________________________
__________________________________________________________________________________________
The following are examples are inverse variations:
Notes: Variations
SOL A1.8
The graphs of an inverse variation will ________________________________________________________
The constant of proportionality in an inverse variation is represented by the _______________________
__________________________________________________________________________________________
k = yx
To see if inverse variation exists:
1. Verify ______________________________________________________________________________
2. ____________________________________________________________________________________
The constant variation is ____________, ____________, ____________, ____________
1st pair
2nd pair
3rd pair
4th pair
Are all products the same? __________________
The inverse variation is ____________________.
The constant variation is ____________, ____________, ____________
1st pair
2nd pair
3rd pair
Are all products the same? __________________
The inverse variation is ____________________.
The constant variation is ____________, ____________, ____________
1st pair
2nd pair
3rd pair
Are all products the same? __________________
Sometimes, if the test for inverse variation doesn’t work, the relation could be a
___________________________________.
The relation is a _______________________ and the equation is _________________
You are trying to build a rectangular garden as the spring approaches. The area that you have to build
it in is 40 feet2. If you want it to have a length of 4 feet, what would the width be? Show or explain how
you got your answer. If you change the length to 8 feet, what is the width? Is this a direct or inverse
variation? Write an equation for this situation.