The given equation is:

\[
y = -\frac{6 \sec(x)}{4}
\]

This simplifies to:

\[
y = -\frac{3 \sec(x)}{2}
\]

Here, \( \sec(x) \) is the secant function, which is the reciprocal of the cosine function, i.e., \( \sec(x) = \frac{1}{\cos(x)} \).

Thus, the equation becomes:

\[
y = -\frac{3}{2 \cos(x)}
\]

This is the simplified form of the given expression. It represents a transformation of the secant function, with a vertical scaling by \( \frac{3}{2} \) and a reflection across the x-axis due to the negative sign.

### Do you need further details or have any questions?

Here are 5 related questions:
1. What is the domain of the secant function?
2. How would the graph of \( y = -\frac{3}{2 \cos(x)} \) look like?
3. What are the vertical asymptotes of the secant function?
4. How do we find the x-intercepts for secant-based functions?
5. How would transformations affect the period of this function?

**Tip**: The secant function has undefined values at the points where the cosine of \(x\) equals zero, leading to vertical asymptotes.

This page explains how to simplify the trigonometric equation y = -6 sec(x) / 4, converting it to y = -3 / (2 cos(x)). Learn about secant function properties, transformations, and key features like vertical asymptotes. Suitable for high school students (Grades 10-12).

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