Determine whether the equation below represents a linear, quadratic, or exponential function.


y=−5x−7*y*=−5*x*−7​


Quadratic

Exponential

Linear

None of these

​​​


Which statement justifies the type of function that it is?

The equation has a variable as an exponent.

The degree of the equation is 11​.

The degree of the equation is 22​.

None of these statements describes the characteristics of the equation.

​


​


Let's analyze the given equation to determine the type of function it represents:

\[
y = -5x - 7
\]

### Step 1: Identify the form of the equation
- **Linear Function:** A linear function has the general form \( y = mx + b \), where \( m \) and \( b \) are constants, and \( x \) is the variable.
- **Quadratic Function:** A quadratic function has the general form \( y = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( x \) is the variable.
- **Exponential Function:** An exponential function has the general form \( y = a \cdot b^x \), where \( a \) and \( b \) are constants, and \( x \) is the exponent.

### Step 2: Analyze the given equation
The equation \( y = -5x - 7 \) is in the form \( y = mx + b \), where \( m = -5 \) and \( b = -7 \). This form matches the general form of a **linear function**.

### Conclusion:
The equation represents a **linear function**.

### Justification:
The correct statement that justifies the type of function is:
**"None of these statements describes the characteristics of the equation."**

This is because:
- The equation does not have a variable as an exponent, so it is not exponential.
- The degree of the equation is 1 (not 11 or 22), which is characteristic of a linear function.

Would you like more details or have any questions about this analysis?

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Here are 5 related questions:
1. How do you determine the degree of a polynomial equation?
2. What are the key characteristics of a quadratic function?
3. Can a linear equation ever include a squared term?
4. How does the presence of an exponent affect the classification of a function?
5. What is the significance of the slope \( m \) in a linear function?

**Tip:** Remember, in a linear equation, the highest power of the variable (degree) is always 1. This is a key characteristic that distinguishes it from quadratic or exponential functions.

Understand how to identify whether an equation represents a linear, quadratic, or exponential function. Analyze the equation y = -5x - 7 step-by-step to determine its function type and learn the key characteristics of linear functions. Suitable for Grades 7-9 students and anyone interested in algebraic functions.

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