To find the equation of a line passing through the points $(2, -4)$ and $(0, -4)$, we start by determining its slope. The slope $m$ is calculated as:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute $(x_1, y_1) = (2, -4)$ and $(x_2, y_2) = (0, -4)$:

$m = \frac{-4 - (-4)}{0 - 2} = \frac{0}{-2} = 0$

A slope of $0$ indicates the line is horizontal. For a horizontal line, the $y$-coordinate is constant. Since both points have a $y$-coordinate of $-4$, the equation of the line is:

$y = -4$

Final Answer:

$y = -4$

Would you like me to explain further or clarify any steps?

Here are 5 related questions for practice:

1. What is the equation of a line with a slope of 0 passing through $(5, 7)$?
2. Write the equation of the vertical line passing through $(3, -6)$.
3. How do you determine the slope of a line given two points?
4. What is the equation of a line with a slope of $-2$ and passing through $(1, 3)$?
5. Find the slope of a line passing through $(-1, 2)$ and $(4, -3)$.

Tip: For horizontal lines, the slope is always 0, and the equation is $y = c$, where $c$ is the $y$-coordinate.