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To find the horizontal asymptote of the function

\[
f(x) = \frac{-7x + 2}{5x + 2}
\]

we need to analyze the degrees of the polynomial in the numerator and the denominator:

1. **Degree of the Numerator (Top)**: The highest power of \( x \) in \(-7x + 2\) is 1.
2. **Degree of the Denominator (Bottom)**: The highest power of \( x \) in \(5x + 2\) is also 1.

Since both the numerator and denominator have the same degree (1), the horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and denominator. In this case:

\[
\text{Horizontal Asymptote} = \frac{\text{Leading coefficient of numerator}}{\text{Leading coefficient of denominator}} = \frac{-7}{5}
\]

### Answer:
The horizontal asymptote is:
\[
y = -\frac{7}{5}
\]

Let me know if you would like further details on this calculation, or if you have any other questions.

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### Related Questions:
1. How do we find vertical asymptotes for rational functions?
2. What are the conditions for a rational function to have no horizontal asymptote?
3. How do oblique asymptotes form in rational functions?
4. Can the horizontal asymptote change if we modify the coefficients of a function?
5. How do asymptotes affect the graph and limits of a function?

### Tip:
For rational functions, when the degrees of the numerator and denominator are equal, the horizontal asymptote is the ratio of the leading coefficients.

Find the horizontal asymptote, if any, of the graph of the rational function f(x) = (-7x + 2) / (5x + 2).

Learn how to find the horizontal asymptote for the rational function f(x) = (-7x + 2) / (5x + 2). This problem uses algebraic techniques and covers key concepts in rational functions and asymptotes, suitable for students in Grades 10-12.

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