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The given equation is:

\[
4y = -2
\]

To find the slope of the line, we first need to rewrite the equation in the slope-intercept form, which is:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept. However, notice that the equation does not involve \( x \), meaning this is a horizontal line.

1. Solve for \( y \):
\[
y = \frac{-2}{4} = -\frac{1}{2}
\]

This is the equation of a horizontal line, where \( y = -\frac{1}{2} \). A horizontal line always has a slope of 0, since there is no change in \( y \) as \( x \) changes.

### Answer:
The slope of the line is \( 0 \).

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the slope of a vertical line?
2. What is the equation of a line with a slope of 0?
3. How can you find the slope given two points on a line?
4. What is the difference between horizontal and vertical lines?
5. How do you convert any general linear equation into slope-intercept form?

**Tip**: Horizontal lines always have a slope of zero, while vertical lines have an undefined slope.

Find the slope of the line determined by the equation 4y = -2.

Learn how to find the slope of a line given the equation 4y = -2. This problem demonstrates key algebraic concepts, including rewriting linear equations and understanding the slope of horizontal lines. Suitable for students in Grades 6-8.

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