The image provides a graph showing a line that passes through the point $(-1, 3)$. To write the point-slope form of the equation, we need two things:

1. A point on the line, which is given as $(-1, 3)$.
2. The slope $m$ of the line.

From the graph, we can determine the slope $m$ by calculating the rise over run. Looking at the line, it drops by 1 unit vertically (rise = $-1$) and moves 1 unit horizontally to the right (run = 1). So, the slope $m = \frac{-1}{1} = -1$.

Now, the point-slope form of a line is given by the equation:

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

Substituting the point $(-1, 3)$ and the slope $m = -1$, the equation becomes:

$y - 3 = -1(x + 1)$

This is the point-slope form for the line.

Would you like more details on this or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you convert a point-slope equation to slope-intercept form?
2. What is the general form of a linear equation?
3. How do you find the slope of a line given two points?
4. Can the point-slope form be used to write the equation of vertical lines?
5. How do you determine the y-intercept from the point-slope form?

Tip: Point-slope form is especially useful when you know a point on the line and the slope but not the y-intercept.