In a certain state, people with an income under $15K pay a minimum income tax plus a % of the amount over $12,750.00.
The table below shows the income, x, and the taxes paid; y for several people.
Using a a linear model, what is the additional % people pay in this state?
Income $ Taxes Pad $
15K 922.50
25K 1,622.50
35K 2,322,50
45K 3,022.50
Possible answers are 6%, 7%, 8%, 9%
x (15,000 - 12,750) = 922.50
x (25,000 - 12,750) = 1622.50
Solve for x in any one of the four situations.
To determine the additional percentage people pay in this state, we need to find the slope of the linear relationship between income and taxes paid.
Let's start by selecting two data points from the table to form two ordered pairs: (x1, y1) = (15, 922.50) and (x2, y2) = (25, 1,622.50).
Next, we can calculate the slope using the formula:
Slope = (change in y) / (change in x)
Slope = (y2 - y1) / (x2 - x1)
Slope = (1,622.50 - 922.50) / (25 - 15)
Slope = (700) / (10)
Slope = 70
The slope represents the additional amount of tax paid for each additional unit of income. In this case, it represents the additional amount paid as a percentage of the income over $12,750.
To convert the slope to a percentage, we need to calculate (70 / 12,750) * 100.
Additional Percentage = (70 / 12,750) * 100
Additional Percentage ≈ 0.549
Therefore, the additional percentage people pay in this state is approximately 0.549%.
None of the provided answers (6%, 7%, 8%, 9%) match this calculation. It's possible that there is an error in the data or the options provided.