Question

The x-axis ranges from 0 to 200,000 in increments of 20,000. The y-axis ranges from 0 to 40 in increments of 10. Four line segments are plotted. The first line segment starts with a closed circle at left parenthesis 0 comma space 10 right parenthesis and ends with a closed circle at approximately left parenthesis 10,000 comma space 10 right parenthesis. The second line segment starts with an open circle at left parenthesis 10,000 comma space 15 right parenthesis and ends with a closed circle at left parenthesis 40,000 comma space 15 right parenthesis. The third line segment starts with an open circle at left parenthesis 40,000 comma space 25 right parenthesis and ends with a closed circle at left parenthesis 91,150 comma space 25 right parenthesis. The fourth line segment starts with an open circle at left parenthesis 91,151 comma space 28 right parenthesis and ends with a closed circle at left parenthesis 190,000 comma space 28 right parenthesis.


A tax preparer needs to explain tax rates to a client. Which of the following best interprets the piecewise linear function for a tax client who earns $65,000?

(1 point)
Responses

The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $37,650. They will be taxed at a rate of 25% for $91,150. They will be taxed at a rate of 28% for $118,000.
The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $37,650. They will be taxed at a rate of 25% for $91,150. They will be taxed at a rate of 28% for $118,000. - no response given

The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $28,375, which is the amount of taxable income within the second step. They will be taxed at a rate of 25% for the remaining $27,350, which is the amount of taxable income within the third step.

Answer 1

The third response.

Explanation: For $65,000 income:
- 10% on the first $9,275
- 15% on the next $28,375 (from $9,275 up to $37,650)
- 25% on the remaining $27,350 (from $37,650 up to $65,000)

(9,275 + 28,375 + 27,350 = 65,000)