October 20, 2014
4.5 Direct Variation
Objective: Write linear equations that represent direct variation.
Direct Variation - when two quantities vary directly.
y = kx
Constant of Variation
Vitruvian Man
Note: To find k, use k=
y
x
Ex:
1) "The length of a man's outspread arms is equal to his height."
2) "The maximum width of the shoulders is a quarter of a man's
height."
Human head proportions
Human body proportion
Direct Variation
y = .25x
y
x = -5
y=x
Not Direct Variation
y = 2x + 1
x y
-1 -2
1 2
36
x y
-1 -4
2 2
4 1
Properties:
October 20, 2014
Ex: Find the constant of variation and slope for y = -3x.
x y
k=
m=
Ex: x and y vary directly.
a) If y = -30 when x = -3, write an equation relating x and y.
b) Find y when x = 8.
Ex: The income of Kathrynn's "Pencils and More" store varies directly
with her advertising budget. When she spends $100/month the gross
monthly income is about $1240. If she spends $250/month on advertising
what can she expect to make?
Try: Based on the table, decide whether forearm lengths
and body height vary directly.
FA 7
7.5 8
8.5 9
BH 52.5 55.6 58.5 63.5 68.4
slide
FindYes
the expected
or No? height of a person
with a forearm length of 10 in.