Let x represent the taxpayer's taxable income and 7 represent the tax. Express the line of the Section D worksheet below as a linear equation in y=mx+b form. Use interval notation to define the income range on which each of your equations is defined.

To express the given tax situation as a linear equation in the form \( y = mx + b \), let's assume:

1. **\( x \)** represents the taxpayer's taxable income.
2. **\( y \)** represents the tax calculated based on income.
3. The worksheet likely involves different income ranges, which could create piecewise linear functions for different intervals.

To proceed, let’s analyze how each line might represent the relationship between income and tax for a specific range of income. Typically, a worksheet like this would use linear expressions of the form:

\[
y = m \cdot x + b
\]

where \( m \) represents the tax rate or slope, and \( b \) is a constant or base amount added for a given income interval.

### Step-by-Step Process

1. **Identify Intervals:** Based on the worksheet, identify income ranges that apply. For example, if one line applies to incomes between \( a \) and \( b \), this interval would be written as \( x \in [a, b) \).

2. **Determine Constants for Each Interval:** Each line may specify a tax amount as a percentage of income plus a fixed dollar amount. For each interval, these values determine \( m \) (the tax rate) and \( b \) (the base tax for that range).

3. **Piecewise Function Structure:** Use the data for each interval to write each linear equation in \( y = mx + b \) form, with the income interval in interval notation.

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Could you provide details or confirm specifics from the Section D worksheet, like income ranges or base tax and tax rates? This would allow for more precise equations.

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1. What specific income ranges and tax rates are provided in the worksheet?
2. Does the worksheet include any additional fixed amounts for each income range?
3. Is the tax rate consistent across intervals, or does it vary with income?
4. Are there any exceptions or special cases mentioned in Section D?
5. Is there a maximum tax limit in this worksheet?

**Tip:** Understanding the slope and intercept in a tax function helps clarify how different income levels affect the overall tax payable.

Learn to express a tax calculation as a linear equation in y=mx+b form. This problem includes setting up linear equations to represent tax based on income ranges, using interval notation to define each income range. Suitable for students in Grades 10-12, it covers linear functions, piecewise functions, and interval notation.

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