https://file.aiquickdraw.com/mathbot/file/1727795997352d4bvpvpa.jpg

The image shows a line on a graph with the point \((-1, 1)\) labeled, and you are asked to write the point-slope form of the line equation using this point.

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

\[
y - y_1 = m(x - x_1)
\]

Where:
- \( (x_1, y_1) \) is the known point on the line.
- \( m \) is the slope of the line.

From the image:
- The slope \( m \) is given as \( -\frac{3}{1} \) (which simplifies to \( -3 \)).
- The point \((-1, 1)\) is labeled.

Using these values, the point-slope form of the line is:

\[
y - 1 = -3(x + 1)
\]

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

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Here are 5 related questions to expand your understanding:

1. How would you convert the point-slope form to slope-intercept form?
2. What happens to the graph if the slope is positive instead of negative?
3. How can you determine the slope of a line just by looking at the graph?
4. How do you find the y-intercept from the point-slope equation?
5. How would the equation change if you used a different point on the line?

**Tip:** Always remember to adjust the signs when substituting points into the point-slope form equation!

Use the labeled point to write a point-slope form for the line.

Learn how to write the point-slope form of a line given a labeled point (-1, 1) and the slope -3. This example covers key concepts in linear equations and is ideal for students in Grades 8-10.

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