Write an equation, in point-slope form, of the line that passes through the given points:
( 1, - 8 ) ( 2, - 5 )

To write the equation of a line in point-slope form, we need to follow these steps:

1. **Find the slope** of the line that passes through the points \((1, -8)\) and \((2, -5)\).  
   The slope formula is:

   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]

   Substituting the given points into the formula:

   \[
   m = \frac{-5 - (-8)}{2 - 1} = \frac{-5 + 8}{1} = \frac{3}{1} = 3
   \]

2. **Use the point-slope form equation**, which is:

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

   We can use either of the given points. Let's use \((1, -8)\):

   \[
   y - (-8) = 3(x - 1)
   \]

3. **Simplify the equation**:

   \[
   y + 8 = 3(x - 1)
   \]

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

Would you like a more detailed explanation, or do you have any other questions?

Here are 5 related questions for further practice:

1. Write the equation in slope-intercept form for the same line.
2. Find the equation of a line passing through the points \((3, 7)\) and \((5, 11)\).
3. Determine the slope of a line that is perpendicular to the line passing through \((1, -8)\) and \((2, -5)\).
4. Write the equation of the line with a slope of 4 that passes through the point \((0, -2)\).
5. Find the point of intersection between the line passing through \((1, -8)\) and \((2, -5)\) and the line \(y = 2x + 3\).

**Tip:** The point-slope form is especially useful when you know a point on the line and its slope, allowing for quick equation writing without rearranging to slope-intercept form immediately.

Learn how to write the equation of a line in point-slope form that passes through the points (1, -8) and (2, -5). This problem covers fundamental concepts in linear equations, including slope calculation and point-slope form application. Suitable for students in Grades 7-9.

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