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Let's solve the problem step-by-step.

### Step 1: Determine the slope of the given line

The given equation of the line is:
\[ 7y - 1 = -2(4 - 2x) \]

First, expand and simplify the equation:
\[ 7y - 1 = -8 + 4x \]

Rearrange to get the equation in slope-intercept form (\(y = mx + b\)):
\[ 7y = 4x + 7 \]
\[ y = \frac{4}{7}x + 1 \]

From this equation, the slope (\(m\)) of the given line is \( \frac{4}{7} \).

### Step 2: Write the equation of the parallel line

Lines that are parallel have the same slope. Thus, the slope of the line that passes through the point \((-8, -6)\) is also \( \frac{4}{7} \).

Using the point-slope form of a line equation, which is \( y - y_1 = m(x - x_1) \) where \((x_1, y_1)\) is a point on the line and \(m\) is the slope, we can plug in the values:
\[ y + 6 = \frac{4}{7}(x + 8) \]

Now simplify this to get the equation in slope-intercept form:
\[ y + 6 = \frac{4}{7}x + \frac{32}{7} \]
\[ y = \frac{4}{7}x + \frac{32}{7} - 6 \]
\[ y = \frac{4}{7}x + \frac{32}{7} - \frac{42}{7} \]
\[ y = \frac{4}{7}x - \frac{10}{7} \]

So, the equation of the line in slope-intercept form is:
\[ y = \frac{4}{7}x - \frac{10}{7} \]

This equation represents the line parallel to the given line and passing through the point \((-8, -6)\).

Would you like more details on any of these steps or have any other questions?

Here are a few related questions you might find interesting:
1. How would you find the perpendicular slope to this line?
2. What would be the equation of a line parallel to the given line but passing through the origin?
3. How can we determine the y-intercept of a line if we know a point and the slope?
4. What is the significance of the slope in real-life applications?
5. Can you find the intersection point between the original line and the y-axis?

**Tip**: When you need to find a line parallel to a given line, always use the same slope for the new line as the given line's slope.

Find the equation of the line which passes through the point (-8, -6) and is parallel to the line 7y - 1 = -2(4 - 2x). Express your answer in slope-intercept form.

Learn how to find the equation of a line parallel to 7y - 1 = -2(4 - 2x) that passes through the point (-8, -6). This problem demonstrates key concepts such as slope-intercept form, parallel line properties, and algebraic simplifications. Suitable for Grades 8-10.

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