To write the equation of a line passing through a given point $(-5, 4)$ with a slope of $-3$, we can use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope,
• $(x_1, y_1)$ is the given point.

Substitute the given values:

• $m = -3$,
• $x_1 = -5$,
• $y_1 = 4$.

This gives the equation:

$y - 4 = -3(x - (-5))$

Simplify the expression:

$y - 4 = -3(x + 5)$

Now distribute the $-3$:

$y - 4 = -3x - 15$

Finally, add 4 to both sides to solve for $y$:

$y = -3x - 11$

Thus, the equation of the line is:

$y = -3x - 11$

Would you like further details on how this form works or any clarifications? Here are some related questions to explore:

1. How does the point-slope form compare to the slope-intercept form?
2. How would the equation change if the slope was positive?
3. What happens if the line passes through the origin (0,0)?
4. How do you graph the equation $y = -3x - 11$?
5. What is the slope of a line perpendicular to this one?

Tip: When writing equations in point-slope form, always ensure to simplify the expressions after substituting values for clarity!