To find the equation of the line in point-slope form, we first need to determine two key pieces of information:

1. The slope of the line (denoted as $m$).
2. A point on the line, which will be the red point shown in the graph.

Step 1: Determine the coordinates of the red point

From the image, the red point appears to be located at $(-6, -4)$.

Step 2: Calculate the slope

To calculate the slope, we need two points on the line. The red point is $(-6, -4)$, and we can estimate another point from the graph, such as $(0, -6)$.

The slope formula is:

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

Substitute the points $(-6, -4)$ and $(0, -6)$ into the formula:

$m = \frac{-6 - (-4)}{0 - (-6)} = \frac{-6 + 4}{0 + 6} = \frac{-2}{6} = -\frac{1}{3}$

Step 3: Write the equation in point-slope form

The point-slope form of a line is:

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

Using the slope $m = -\frac{1}{3}$ and the red point $(-6, -4)$, the equation becomes:

$y - (-4) = -\frac{1}{3}(x - (-6))$

Simplify the equation:

$y + 4 = -\frac{1}{3}(x + 6)$

Final equation:

$y + 4 = -\frac{1}{3}(x + 6)$

Would you like to go over any steps in detail or ask for further clarification?

Here are 5 follow-up questions related to this:

1. How do we convert the point-slope form to slope-intercept form?
2. What is the significance of the slope being negative in this example?
3. How can you verify the slope by choosing other points on the line?
4. What are the advantages of using point-slope form versus other forms of the equation of a line?
5. How do you handle a vertical line when writing an equation?

Tip: Always remember that the slope represents the steepness of the line; a positive slope rises, while a negative slope falls as you move along the x-axis.