The image shows a task asking to write the equation of a line in point-slope form based on the graph. From the graph, the line appears to pass through the point (-2, 3) and has a downward slope.

To solve this, we follow these steps:

Step 1: Identify the formula for point-slope form

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.

Step 2: Identify a point on the line

From the graph, one labeled point is $(-2, 3)$, which gives us $(x_1, y_1) = (-2, 3)$.

Step 3: Calculate the slope $m$

To find the slope, select another point on the line. The line also passes through $(2, -1)$.

The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{2 - (-2)} = \frac{-4}{4} = -1$

Step 4: Write the equation

Substitute the point $(-2, 3)$ and the slope $m = -1$ into the point-slope form: $y - 3 = -1(x - (-2))$ Simplifying: $y - 3 = -1(x + 2)$

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

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. How would you convert the point-slope form to slope-intercept form?
2. What is the slope-intercept form of the equation from this graph?
3. How do you determine the slope if the line is vertical or horizontal?
4. Can you find another point on the line and verify the slope?
5. How does the point-slope form change if you pick a different point on the line?

Tip: Always double-check the slope calculation by carefully selecting points that are clear intersections on the graph grid!