To find the equation of the line in point-slope form, we need to determine two main components: the slope of the line and a point on the line, as point-slope form is given by:

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

where $(x_1, y_1)$ is a point on the line, and $m$ is the slope.

Step 1: Identify a Point on the Line

The red point on the graph is located at $(0, 2)$.

Step 2: Calculate the Slope

To find the slope $m$, we need two points on the line. From the graph, we can identify the red point $(0, 2)$ and another point, such as $(8, 0)$, where the line crosses the x-axis.

The slope formula is:

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

Using the points $(0, 2)$ and $(8, 0)$:

$m = \frac{0 - 2}{8 - 0} = \frac{-2}{8} = -\frac{1}{4}$

Step 3: Write the Equation in Point-Slope Form

Now, we substitute the red point $(0, 2)$ and the slope $-\frac{1}{4}$ into the point-slope form:

$y - 2 = -\frac{1}{4}(x - 0)$

or simply:

$y - 2 = -\frac{1}{4}x$

This is the equation of the line in point-slope form.

Would you like more details or have any questions?

Here are some related questions for practice:

1. How would you convert this equation to slope-intercept form?
2. What is the slope of a line perpendicular to this one?
3. How would you find the y-intercept of this line?
4. What is the equation in point-slope form if a different point on the line was used?
5. How can we find the x-intercept from this equation?

Tip: In point-slope form, use any point on the line and the slope to write the equation quickly.