We need to find the horizontal asymptote of the function $f(x) = \frac{2x - 7}{5x + 3}$.

1. Problem Description

We need to find the horizontal asymptote of the function $f(x) = \frac{2x - 7}{5x + 3}$.

2. Solution Steps

To find the horizontal asymptote of a rational function, we examine the limit of the function as $x$ approaches infinity.

If the degree of the numerator and the degree of the denominator are the same, then the horizontal asymptote is the ratio of the leading coefficients.

In this case, the degree of the numerator $2x - 7$ is 1, and the degree of the denominator $5x + 3$ is also

1. The leading coefficient of the numerator is 2, and the leading coefficient of the denominator is

5. Therefore, the horizontal asymptote is $y = \frac{2}{5}$.

$$\lim_{x \to \infty} \frac{2x - 7}{5x + 3} = \lim_{x \to \infty} \frac{x(2 - \frac{7}{x})}{x(5 + \frac{3}{x})} = \lim_{x \to \infty} \frac{2 - \frac{7}{x}}{5 + \frac{3}{x}} = \frac{2 - 0}{5 + 0} = \frac{2}{5}$$

The horizontal asymptote is $y = \frac{2}{5}$.

3. Final Answer

$y = \frac{2}{5}$