Notes 8.2 Variation.notebook
February 24, 2015
8.2 Quiz:
1.
What is the horizontal asymptote?
y = 2.
What value is not in the domain? Answers:
1. 1 2. 2 Notes 8.2 Variation.notebook
February 24, 2015
Notes 11 ‐ 1: Variation
Direct Variation
Equation
y = kx
"y varies directly as x"
Notes 8.2 Variation.notebook
February 24, 2015
Inverse Variation
Equation
k
y = x
"y varies inversely as x"
Notes 8.2 Variation.notebook
February 24, 2015
Joint Variation
Equation
y = kxz "y varies jointly as x and z"
Notes 8.2 Variation.notebook
Do x and y vary inversely or directly?
x
2. y + x = 3
1. xy = 4
3. y = 5
February 24, 2015
Notes 8.2 Variation.notebook
February 24, 2015
Notes 8.2 Variation.notebook
February 24, 2015
The variables x and y vary inversely. Use the given
values to find an equation that relates the variables.
4. x = 3, y = 4
5. x = -5, y = 7
Notes 8.2 Variation.notebook
February 24, 2015
6. Seesaw ­ To balance a seesaw, the distance, d (in feet), a person is from the fulcrum is inversely proportional to his or her weight, w (in pounds). David, who weighs 190 pounds, is sitting 6 feet away from the fulcrum. Stacey weighs 105 pounds. How far from the fulcrum must she sit to balance the seesaw?
Notes 8.2 Variation.notebook
February 24, 2015
Joint and Mixed Variation
7. x varies jointly as y and √z. x = 24 when y = 4 and z = 9.
Step 1: Set up equation
Find x when y = 7 and z = 4.
Step 2: Plug in #'s to find k
Step 3: Plug in k to write equation
Step 4: Solve for the variable
8. y varies directly as x 2 and inversely as z. y = 2 when x = 3
and z = 27. Find y when x = 2 and z = 3.
Notes 8.2 Variation.notebook
February 24, 2015
9. x varies jointly as y and z 2. x = 2 when y = 4 and z = 3. Find
x when y = 8 and z = 5.
10. The area, A, of an ellipse varies jointly with the length of the
major axis, M, and the length of the minor axis, m. An ellipse that
has a major axis of 2 cm and a minor axis of 1 cm has an area of
1.57 cm2. Write an equation that relates the variables.
Notes 8.2 Variation.notebook
February 24, 2015