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.

Learn how to find the equation of a line that passes through the points (-8, -4) and (-2, 5). This step-by-step solution involves calculating the slope and using the point-slope form to derive the final equation. Ideal for students in Grades 8-10 studying linear equations.

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