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Let's solve this step by step.

You are asked to find the equation of the line that passes through the points (-2, 5) and (6, 3) using the point-slope form.

### Steps:

1. **Find the slope (m)**:
   The slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]

   Using \((-2, 5)\) as \((x_1, y_1)\) and \((6, 3)\) as \((x_2, y_2)\):
   \[
   m = \frac{3 - 5}{6 - (-2)} = \frac{-2}{6 + 2} = \frac{-2}{8} = -\frac{1}{4}
   \]
   So, the slope \(m = -\frac{1}{4}\).

2. **Use the point-slope formula**:
   The point-slope form of a line is given by:
   \[
   y - y_1 = m(x - x_1)
   \]
   We can use either of the two points. Let's use \((6, 3)\) as \((x_1, y_1)\), and substitute the values:
   \[
   y - 3 = -\frac{1}{4}(x - 6)
   \]

3. **Simplify the equation** (if necessary, but point-slope form allows leaving it in this format).

The final equation in point-slope form is:
\[
y - 3 = -\frac{1}{4}(x - 6)
\]

If you have any questions or need further clarification, feel free to ask!

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Here are 5 related questions to expand your understanding:
1. How can you convert this point-slope form into slope-intercept form?
2. What is the equation of a line perpendicular to this line passing through the point (6, 3)?
3. What happens to the slope if you change one of the points?
4. Can you find the equation of a line parallel to this one that passes through the origin?
5. How would you find the x- and y-intercepts of the line from the point-slope form?

**Tip:** The slope tells you how steep the line is, and whether it's increasing or decreasing!

The points (-2, 5) and (6, 3) fall on a particular line. What is its equation in point-slope form?

This problem explains how to find the equation of a line in point-slope form, given the points (-2, 5) and (6, 3). Learn to calculate the slope and apply the point-slope formula step-by-step, suitable for students in Grades 8-10.

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