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.