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The problem asks to find the equation of a line in slope-intercept form, given two points: \((5, 1)\) and \((2, -2)\).

### Steps:
1. **Calculate the slope (m)** using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the given points:
   \[
   m = \frac{-2 - 1}{2 - 5} = \frac{-3}{-3} = 1
   \]

2. **Use the point-slope formula** to find the equation of the line. The point-slope formula is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using the point \((5, 1)\) and slope \(m = 1\):
   \[
   y - 1 = 1(x - 5)
   \]
   Simplifying:
   \[
   y - 1 = x - 5
   \]
   Add 1 to both sides:
   \[
   y = x - 4
   \]

### Final answer:
The equation of the line in slope-intercept form is:
\[
y = x - 4
\]

Would you like more details on any part of the solution or have any other questions?

Here are 5 related questions to consider:
1. How would the equation change if one of the points was different?
2. What is the geometric meaning of the slope?
3. How can we find the x- and y-intercepts from this equation?
4. What happens if the slope were negative?
5. How can the distance between the two points be calculated?

**Tip:** The slope of a line describes how steep the line is. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.

Use the point-slope formula to write an equation of the line given the following information. The line passes through the points (5, 1) and (2, -2). Write the final answer in slope-intercept form.

Learn how to find the equation of a line passing through the points (5, 1) and (2, -2) using the slope and point-slope formula, then converting it to slope-intercept form. This detailed solution includes the calculation of the slope and the equation of the line. Ideal for Grades 7-9.

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