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To find the equation of the line passing through the points \((-5, -3)\) and \( (5, -2) \), we will use the point-slope form of the equation of a line:

1. **Calculate the slope (m):**
   The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the given points \((-5, -3)\) and \((5, -2)\):
   \[
   m = \frac{-2 - (-3)}{5 - (-5)} = \frac{-2 + 3}{5 + 5} = \frac{1}{10}
   \]

2. **Use the point-slope form:**
   The point-slope form of the equation of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using the slope \(m = \frac{1}{10}\) and one of the points \((-5, -3)\):
   \[
   y - (-3) = \frac{1}{10}(x - (-5))
   \]
   Simplify:
   \[
   y + 3 = \frac{1}{10}(x + 5)
   \]
   \[
   y + 3 = \frac{1}{10}x + \frac{1}{2}
   \]

3. **Solve for \(y\):**
   \[
   y = \frac{1}{10}x + \frac{1}{2} - 3
   \]
   \[
   y = \frac{1}{10}x + \frac{1}{2} - \frac{6}{2}
   \]
   \[
   y = \frac{1}{10}x - \frac{5}{2}
   \]

Thus, the equation of the line in terms of \(x\) is:
\[
y = \frac{1}{10}x - \frac{5}{2}
\]

Would you like more details or have any questions?

Here are 5 questions you might ask next:
1. How do you find the equation of a line given the slope and a point?
2. What is the point-slope form of a linear equation?
3. How can I convert the point-slope form to the slope-intercept form?
4. What is the standard form of a linear equation?
5. How do you find the slope of a line given two points?

**Tip:** When finding the equation of a line, always start by calculating the slope, then use the point-slope form to derive the equation.

Learn how to find the equation of a line passing through the points (-5, -3) and (5, -2) using the point-slope form. This problem involves calculating slope, using the point-slope formula, and converting to slope-intercept form. Suitable for high school students.

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