1. 6-2 MODELING TAX SCHEDULES
Banking
5/9/2019
6-2 MODELING TAX SCHEDULES
OBJECTIVES
Construct income tax graphs using compound equations. CCSS: F.IF.1, F.IF.2, F.IF.7b, F.IF.8, F.BF.1a This is Jeopardy!!!: This is how a progressive sales tax system differs from the current sales tax system.
Chapter 1

2. Key Terms flat tax proportional tax progressive tax system tax bracket
regressive tax schedule

3. How can you graph tax schedules?
How would sales tax work if it was a progressive rather than a proportional tax?
How much tax would a shopper pay if he or she needed to make a $100 purchase and the tax schedule was:
6% on the first $50
8% on any amount over $50
Describe how a progressive sales tax system is different than the current sales tax system.

4. Example 1
Model the schedule shown in tax schedule notation in interval notation.

5. Example 1
Flat, or Proportional, Tax: a tax that has the same percent for all amounts

6. Progressive Tax System: the tax rate increases as the income increases
Example 1
Flat, or Proportional, Tax: a tax that has the same percent for all amounts
Progressive Tax System: the tax rate increases as the income increases

7. Progressive Tax System: the tax rate increases as the income increases
Example 1
Flat, or Proportional, Tax: a tax that has the same percent for all amounts
Progressive Tax System: the tax rate increases as the income increases
Tax Bracket: each line of the tax schedule has an increasing percent depending on increasing income

8. Example 1
Model the schedule shown in tax schedule notation in interval notation.

9. Example 1 CHECK YOUR UNDERSTANDING
Write the tax schedule notation and interval notation that would apply to an income of $172,

10. Example 2
Tax Equation

11. Example 2
Tax Equation y = income tax, x = income

12. Example 2
Tax Equation y = income tax, x = income

13. Example 2
Tax Equation y = income tax, x = income

14. Example 2
Tax Equation y = income tax, x = income

15. Example 2
Tax Equation y = income tax, x = income

16. Example 2
Tax Equation y = income tax, x = income

17. Example 3
Express the equations in the married taxpayers filing jointly schedule in y = mx + b form.

18. Example 2
How does the piecewise function relate to the tax computation worksheet?

19. Example 2 CHECK YOUR UNDERSTANDING
The tax equation for incomes over $230,450 but not over $411,500 is y = 51, (x − 230,450). Simplify the equation and explain the numerical significance of the slope and the y-intercept.

20. Example 3 CHECK YOUR UNDERSTANDING
Use the appropriate equation from Example 3 to determine the tax for an income of $46,000.

21. Example 4
Examine the piecewise function f(x) composed of the first three equations in Example 3. Graph the function on the appropriate interval.
f(x) =
0.10x 0 < x ≤ 18,450
0.15x − ,450 < x ≤ 74,900
0.25x − 8, ,900 < x ≤ 151,200

22. Example 4
f(x) =
0.10x 0 < x ≤ 18,450
0.15x − ,450 < x ≤ 74,900
0.25x − 8, ,900 < x ≤ 151,200

23. Example 4 CHECK YOUR UNDERSTANDING
If you were to graph the fourth equation in the piecewise function, y = 0.28x − 12,948.50, where would you expect the last point in that equation to be? Explain your reasoning.

24. Example 4 EXTEND YOUR UNDERSTANDING
What are the monetary implications of the fact that the slope of the last segment of the piecewise function is greater than the slope of the segment preceding it?