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?

---

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.