1. You will need: calculator
Date:
1.10 Notes: Variation
Lesson Objective: Write mathematical models for direct, inverse and joint variation.
You will need: calculator
Real-World App: What is the Pennsylvania state tax?

2. Lesson 1: Direct Variation
Direct Variation: y varies directly as x or y is directly proportional to x.
y = kx
k is the constant of variation or the constant of proportionality.

3. Lesson 1: Direct Variation
In Pennsylvania, the state income tax is directly proportional to gross income. Suppose you are working in Pennsylvania and your state income tax deduction is $46.05 for a gross monthly income of $ Find a mathematical model that gives the Pennsylvania state income tax in terms of gross income.

4. Lesson 2: Direct Variation as nth Power
y = kxn
for some constant k and input x is repeated n times.

5. Lesson 2: Direct Variation as nth Power
The distance a ball rolls down an inclined plane is directly proportional to the square of the time it rolls. During the first second, the ball rolls 8’.
Write an equation relating the distance traveled to the time.
B. How far will the ball roll during the first 3 seconds?

6. Lesson 3: Inverse Variation
y = 𝑘 𝑥
y varies inversely as x or y is inversely propor-tional to x.
As one variable increases, the other decreases.

7. Lesson 3: Direct and Inverse Variation Together

8. Lesson 4: Joint Variation
z = kxnym
z varies jointly as x and y or is jointly propor-tional to x and y.
Both x and y affect the outcome of z.

9. Lesson 4: Joint Variation

10. 1.10: DIGI Yes or No
Find the mathematical model representing the statement. Find k. 1. 2. 3. 4.