Write the equation of a line in general form that passes through the points (-3,6) and (5,-10) 

To find the equation of a line in general form, we follow these steps:

1. **Find the slope (m)** using the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the points \((-3, 6)\) and \((5, -10)\):
   \[
   m = \frac{-10 - 6}{5 - (-3)} = \frac{-16}{5 + 3} = \frac{-16}{8} = -2
   \]
   So, the slope \(m = -2\).

2. **Use the point-slope form of a line** to write the equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using one of the points, say \((-3, 6)\), and the slope \(m = -2\):
   \[
   y - 6 = -2(x + 3)
   \]
   Simplifying:
   \[
   y - 6 = -2x - 6
   \]
   \[
   y = -2x
   \]

3. **Convert to general form** \(Ax + By + C = 0\):
   \[
   2x + y = 0
   \]
   This is the equation of the line in general form.

Would you like any further clarifications on this solution?

Here are 5 related questions to expand your understanding:
1. How do you determine the slope when the points are given as fractions?
2. Can you find the equation of a vertical line through two points?
3. How does the slope of a line relate to its steepness?
4. What happens to the equation of the line when the points are very close together?
5. How can you convert a general form equation to slope-intercept form?

**Tip:** Always verify your solution by substituting the points back into the final equation to ensure they satisfy it.

Write the equation of a line in general form that passes through the points (-3,6) and (5,-10).

Learn how to find the equation of a line in general form that passes through the points (-3,6) and (5,-10). This solution covers key algebraic concepts such as finding the slope, using the point-slope form, and converting to the general form. Suitable for students in Grades 8-10.

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