To write the equation of a line in slope-intercept form, $y = mx + b$, we first need to find the slope $m$ and then determine the $y$-intercept $b$.

Step 1: Calculate the slope ($m$)

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Given the points $(-8, 9)$ and $(-2, -9)$, let's plug them into the formula:

$m = \frac{-9 - 9}{-2 - (-8)} = \frac{-18}{-2 + 8} = \frac{-18}{6} = -3$

So, the slope $m = -3$.

Step 2: Find the $y$-intercept ($b$)

Now that we know the slope is $-3$, we use one of the points to find the $y$-intercept. We'll use the point $(-8, 9)$. Substituting into the equation $y = mx + b$:

$9 = -3(-8) + b$

Simplify:

$9 = 24 + b$

Solve for $b$:

$b = 9 - 24 = -15$

Step 3: Write the equation

Now that we have the slope $m = -3$ and the intercept $b = -15$, the equation of the line is:

$y = -3x - 15$

Would you like further explanation or have any questions?

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Here are 5 related questions for practice:

1. What is the equation of a line that passes through $(1, 2)$ and $(4, 5)$?
2. How do you find the slope between two points if both points have the same $y$-coordinate?
3. Can you rewrite the equation $y = -3x - 15$ in standard form?
4. What happens to the slope if the two points have the same $x$-coordinate?
5. How would you find the equation of a line parallel to $y = -3x - 15$ that passes through $(0, 5)$?

Tip: The slope of a line measures its steepness; a negative slope means the line goes down as you move to the right.