Algebra 2 Notes
May 19, 2009
Warm-Ups
Remembering Direct Variation
If you need help remembering, refer to page 74
Example 4
y varies directly with x:
a) Given that x = 2 when y = 4, find y when x = 5
b) Given that x = 1 when y = 5, find y when x = 3
c) Given that x = 10 when y = 3, find y when x = 4
Direct Variation vs. Indirect Variation
 Direct Variation:
 x and y vary directly with each other
 When one variable increases, the other increases as well
 When one variable decreases, the other decreases as well
 Indirect Variation:
 x and y vary inversely with each other
 When one variable increases, the other decreases
Direct Variation vs. Indirect Variation
 If it is direct variation, x divided by y will be the same
for all values
 If it is inverse variation x times y will be the same for
all values
Are the following examples inverse variation, direct
variation, or neither?
x
y
x
y
x
y
0.5
2
6
1.5
6
18
0.2
0.6
1.2
12
4
2
1
2
3
2
1
0.5
Writing an Equation
Ex 1) Suppose that x and y vary inversely, and x = 3
when y = -5. Write the function that models the
inverse variation.
(First find the value for k, then plug that into
Ex 2) Suppose that x and y vary inversely, and x = 0.3
when y = 1.4. write the function that models the
inverse variation
)
Joint Variation Page 490
Combined Variation
z varies jointly with x and y
z varies jointly with x and y and
inversely with w.
z varies directly with x and inversely
with wy.
Equation Form
Real World Connection
 Physics: Newton’s Law of Universal Gravitation is
modeled by the following formula:
F is the gravitational force between two objects with
masses m1 and m2, and d is the distance between the two
objects. G is the gravitational constant. Describe
Newton’s law as a combined variation:
F varies jointly with __________
F varies inversely with __________
Homework #63
Page 491 #1, 4, 7, 8, 12, 13, 17,
18, 23, 24, 27, 60-62