To determine whether the point $(-2, -4)$ lies on the line described by the equation $\frac{1}{2}x + y = -5$, we substitute $x = -2$ and $y = -4$ into the equation and check if the equality holds:

Substituting the values:

$\frac{1}{2}(-2) + (-4) = -5$

Simplify: $\frac{1}{2}(-2) = -1$

$-1 + (-4) = -5$

$-5 = -5$

Since the equation is satisfied, the point $(-2, -4)$ is on the line.

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Would you like a detailed explanation of the solution or have any other questions? Here are 5 related questions to consider:

1. How do you determine if a point lies on a curve or line for any equation?
2. What is the slope of the line given by the equation $\frac{1}{2}x + y = -5$?
3. How would you graph this line and verify the point visually?
4. What are other points that satisfy this line's equation?
5. How do you convert the given equation into slope-intercept form?

Tip: Always substitute carefully into equations to avoid simple errors when verifying solutions.