To find the equation of the line that passes through the points $(-5, -1)$ and $(-2, -8)$, we need to follow these steps:

Step 1: Find the slope (m)

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

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

Using the points $(-5, -1)$ and $(-2, -8)$:

$m = \frac{-8 - (-1)}{-2 - (-5)} = \frac{-8 + 1}{-2 + 5} = \frac{-7}{3}$

So, the slope $m = -\frac{7}{3}$.

Step 2: Use the point-slope form to write the equation

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

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

We can use either point, but let's use $(-5, -1)$:

$y - (-1) = -\frac{7}{3}(x - (-5))$

Simplifying this equation:

$y + 1 = -\frac{7}{3}(x + 5)$

Distribute the slope:

$y + 1 = -\frac{7}{3}x - \frac{35}{3}$

Now, subtract 1 from both sides:

$y = -\frac{7}{3}x - \frac{35}{3} - 1$

Convert 1 to a fraction:

$y = -\frac{7}{3}x - \frac{35}{3} - \frac{3}{3}$

Finally:

$y = -\frac{7}{3}x - \frac{38}{3}$

The equation of the line is:

$y = -\frac{7}{3}x - \frac{38}{3}$

Would you like more details, or do you have any questions about this process?

Here are five related questions to explore:

1. How can you find the slope if the two points are vertically aligned?
2. How would the equation change if the points were reversed?
3. Can you rewrite the equation in standard form $Ax + By = C$?
4. What happens to the slope if the two points are closer together?
5. How can you verify if a third point lies on the same line?

Tip: When working with fractions in linear equations, always simplify terms before combining them for accuracy.