Write the equation of the line that passes through the points left parenthesis, minus, 3, comma, minus, 8, right parenthesis(−3,−8)and left parenthesis, minus, 9, comma, 9, right parenthesis(−9,9). Put your answer in fully simplified *point-slope* form,

To find the equation of the line passing through the points \((-3, -8)\) and \((-9, 9)\) in point-slope form, we’ll follow these steps:

1. **Calculate the slope** \((m)\) using the formula:

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

   Here, \((x_1, y_1) = (-3, -8)\) and \((x_2, y_2) = (-9, 9)\).

   \[
   m = \frac{9 - (-8)}{-9 - (-3)} = \frac{9 + 8}{-9 + 3} = \frac{17}{-6} = -\frac{17}{6}
   \]

2. **Use the point-slope form of the line equation**: 

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

   Choosing the point \((-3, -8)\), we substitute \(m = -\frac{17}{6}\), \(x_1 = -3\), and \(y_1 = -8\):

   \[
   y - (-8) = -\frac{17}{6}(x - (-3))
   \]

   Simplify this to:

   \[
   y + 8 = -\frac{17}{6}(x + 3)
   \]

So, the equation of the line in point-slope form is:

\[
y + 8 = -\frac{17}{6}(x + 3)
\]

Would you like further explanation or details?

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### Related Questions
1. How do you convert a point-slope form equation to slope-intercept form?
2. What is the significance of the slope in a line equation?
3. How can you verify if a point lies on a given line?
4. How do you find the midpoint between two points?
5. What are alternative forms of linear equations?

### Tip
When using point-slope form, you can choose either of the two given points for \(x_1\) and \(y_1\); both will give the same line equation.

Write the equation of the line that passes through the points (-3, -8) and (-9, 9). Put your answer in fully simplified point-slope form.

Discover how to derive the equation of a line in point-slope form that passes through the points (-3, -8) and (-9, 9). This problem emphasizes key concepts in algebra, particularly the slope and point-slope form, suitable for Grades 8-10.

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