To find the equation of the line passing through the points $(-8, 9)$ and $(-2, -9)$, we need to follow these steps:

Step 1: Calculate the slope (m)

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

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

Substitute the given points $(-8, 9)$ and $(-2, -9)$:

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

So, the slope $m = -3$.

Step 2: Use the point-slope form

The equation of a line in point-slope form is:

$y - y_1 = m(x - x_1)$

We can use one of the given points, say $(-8, 9)$, and substitute the slope $m = -3$ into the equation:

$y - 9 = -3(x + 8)$

Step 3: Simplify to slope-intercept form

Now, let's simplify this equation into the slope-intercept form $y = mx + b$.

$y - 9 = -3(x + 8)$ $y - 9 = -3x - 24$ $y = -3x - 24 + 9$ $y = -3x - 15$

Final equation

The equation of the line in slope-intercept form is:

$y = -3x - 15$

Would you like any further explanation on this?

Here are 5 related questions for further practice:

1. How do you find the equation of a line when given the slope and a point?
2. What is the meaning of the slope in the context of a line?
3. How can you convert a line from standard form to slope-intercept form?
4. How do you determine if two lines are parallel or perpendicular using their slopes?
5. How do you find the x-intercept and y-intercept of a line?

Tip: Always double-check the slope calculation before proceeding with the equation to avoid mistakes.