The equation is to be written in point-slope form, which is given by the formula:

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

Where:

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

From the image, we are given:

• Slope $m = -3$
• Point $(x_1, y_1) = (2, -4)$

Substituting these values into the point-slope form:

$y - (-4) = -3(x - 2)$

Simplify the equation by removing double negatives:

$y + 4 = -3(x - 2)$

This is the equation in point-slope form.

Do you want further details or have any questions?

Here are 5 related questions for deeper understanding:

1. How do you convert point-slope form to slope-intercept form?
2. What happens if the slope is zero? How does the equation change?
3. How would you graph this line based on the equation?
4. Can you rewrite this equation if the slope was positive 3 instead of negative 3?
5. What is the general form of a linear equation, and how do you convert to it from point-slope form?

Tip: Always double-check the signs when working with negative slopes and coordinates, as it can be easy to overlook double negatives!