The given equation of the line is:

$y + \frac{3}{4}x + 2 = 0$

To find the slope of this line, rearrange it into the slope-intercept form ($y = mx + b$):

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

Here, the slope ($m$) is $-\frac{3}{4}$.

A line parallel to this one will have the same slope, $-\frac{3}{4}$. Using the point-slope form of a line equation:

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

where $(x_1, y_1) = (8, 2)$ and $m = -\frac{3}{4}$, substitute the values:

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

Simplify the equation:

$y - 2 = -\frac{3}{4}x + 6$

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

Thus, the equation of the line is:

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

Would you like a graphical representation or further explanation of parallel line equations?

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5 Related Questions:

1. How do you derive the equation for a line perpendicular to the given line passing through the same point?
2. What are the conditions for two lines to be parallel?
3. How would the equation change if the line passed through a different point, like (3, 5)?
4. Can you explain the difference between the point-slope form and the slope-intercept form of a line?
5. How do you determine if a point lies on a given line?

Tip:

Always check the slope of a line to quickly identify if two lines are parallel ($m_1 = m_2$) or perpendicular ($m_1 \cdot m_2 = -1$).