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\( y = x - 7 \) is a linear algebraic equation.
Solution
**2. \( y = x - 7 \)**
**Classification:** *Algebraic Equation*
**Explanation:**
An **algebraic equation** is any equation that involves only algebraic expressions, which include polynomials and their operations (addition, subtraction, multiplication, division, and non-negative integer exponents).
The equation \( y = x - 7 \) is a **linear equation**, which is a specific type of algebraic equation. Here's why:
- **Degree:** The highest power of the variable \( x \) is 1, making it a first-degree polynomial.
- **Form:** It follows the standard linear form \( y = mx + b \), where \( m \) and \( b \) are constants.
- **Operations:** It involves only addition and subtraction of algebraic terms.
Since it satisfies all the conditions of an algebraic equation by involving a linear (polynomial of degree one) relationship between \( x \) and \( y \), \( y = x - 7 \) is indeed an algebraic equation.
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Simplify this solution Bonus Knowledge
Did you know that linear equations like \( y = x - 7 \) can be graphed on a coordinate plane as a straight line? This particular equation has a slope of 1 and a y-intercept at -7, meaning it crosses the y-axis at the point (0, -7). This visual representation is a powerful way to understand relationships between two variables! In real life, equations like this can model various situations, such as either tracking expenses, where \( y \) could represent your remaining budget based on \( x \) number of items purchased minus a set cost. It’s a straightforward way to keep your finances on track! So, next time you see a linear equation, think about the practical scenarios it could represent!
