To find the equation of the line that passes through the points $(-8, -4)$ and $(-2, 5)$, we can follow these steps:

1. Find the slope $m$

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

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

Substituting the values from the points $(-8, -4)$ and $(-2, 5)$:

$m = \frac{5 - (-4)}{-2 - (-8)} = \frac{5 + 4}{-2 + 8} = \frac{9}{6} = \frac{3}{2}$

So, the slope $m = \frac{3}{2}$.

2. Use point-slope form to find the equation of the line

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

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

Using the point $(-8, -4)$ and the slope $m = \frac{3}{2}$, we can substitute into this formula:

$y - (-4) = \frac{3}{2}(x - (-8))$

Simplifying this:

$y + 4 = \frac{3}{2}(x + 8)$

3. Distribute and solve for $y$

Now distribute $\frac{3}{2}$ on the right-hand side:

$y + 4 = \frac{3}{2}x + \frac{3}{2} \times 8$ $y + 4 = \frac{3}{2}x + 12$

Subtract 4 from both sides:

$y = \frac{3}{2}x + 12 - 4$ $y = \frac{3}{2}x + 8$

Final Equation:

The equation of the line is:

$y = \frac{3}{2}x + 8$

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Would you like further details on how we arrived at this, or have any specific questions?

Here are 5 related questions to practice:

1. Find the equation of a line passing through $(1, 2)$ and $(3, 7)$.
2. What is the slope of the line passing through $(4, -3)$ and $(-6, 9)$?
3. Determine if the points $(2, 4)$, $(4, 8)$, and $(6, 12)$ are collinear.
4. Find the equation of a line with a slope of 4 that passes through the point $(1, -2)$.
5. What is the distance between the points $(-2, 5)$ and $(3, -1)$?

Tip: When finding the slope, pay attention to the signs of the coordinates to avoid mistakes with negative values.