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To find the equation of the line passing through the points \((-1, -6)\) and \((1, -2)\), we will follow these steps:

### Step 1: Calculate the slope (m)
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points \((-1, -6)\) and \((1, -2)\):
\[
m = \frac{-2 - (-6)}{1 - (-1)} = \frac{-2 + 6}{1 + 1} = \frac{4}{2} = 2
\]
Thus, the slope \( m = 2 \).

### Step 2: Use the point-slope form
The equation of a line with slope \(m\) passing through a point \((x_1, y_1)\) is given by the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-1, -6)\) and the slope \(m = 2\):
\[
y - (-6) = 2(x - (-1))
\]
This simplifies to:
\[
y + 6 = 2(x + 1)
\]

### Step 3: Simplify to slope-intercept form
Now, expand and simplify the equation:
\[
y + 6 = 2(x + 1)
\]
\[
y + 6 = 2x + 2
\]
\[
y = 2x + 2 - 6
\]
\[
y = 2x - 4
\]

Thus, the equation of the line is:
\[
y = 2x - 4
\]

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What would the equation of the line be if it passed through the points \((0, 0)\) and \((1, 2)\)?
2. How do we find the y-intercept directly from the point-slope form?
3. How can you verify if another point lies on this line?
4. How do you convert from point-slope form to standard form?
5. What is the significance of the slope in the context of the line's steepness?

**Tip:** Always check your final equation by substituting the points back into it to ensure both satisfy the equation.

Find the equation (in terms of x) of the line through the points (-1, -6) and (1, -2)

Learn how to find the equation of the line passing through the points (-1, -6) and (1, -2). This algebra problem includes using the slope formula and converting to slope-intercept form. Suitable for Grades 8-10.

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