The problem asks to write the point-slope form of the line using the labeled point. From the image, the labeled point is $(-2, 1)$.

Step 1: Find the Slope

From the graph, we can see that the slope ($m$) can be calculated using the change in $y$ over the change in $x$:

• Pick two points: $(-2, 1)$ and $(0, -3)$.
• Calculate the slope:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 1}{0 - (-2)} = \frac{-4}{2} = -2$

Step 2: Write the Point-Slope Form

The point-slope form of a line is given by:

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

Substitute the point $(-2, 1)$ and the slope $m = -2$:

$y - 1 = -2(x - (-2))$

Simplifying:

$y - 1 = -2(x + 2)$

Final Answer:

The point-slope form of the line is:

$y - 1 = -2(x + 2)$

Would you like further details or have any questions about this solution? Here are five related questions you might want to explore:

1. How do you convert the point-slope form to the slope-intercept form?
2. What is the slope-intercept form of the given line?
3. How do you find the slope given two points without a graph?
4. What are the characteristics of lines with a negative slope?
5. How would the point-slope form change if the line passed through $(-4, 3)$?

Tip: Point-slope form is most useful when you know the slope and one point on the line.