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The problem asks to find the equation of a line that passes through the point \((-2, 2)\) and is parallel to the line given by the equation:

\[
2x - 4y - 8 = 0
\]

### Step 1: Determine the slope of the given line
The general form of a line is \(Ax + By + C = 0\). To find the slope, we rewrite the equation of the line in slope-intercept form \(y = mx + b\), where \(m\) is the slope.

Starting with the equation:
\[
2x - 4y - 8 = 0
\]

Solve for \(y\):
\[
-4y = -2x + 8
\]
\[
y = \frac{1}{2}x - 2
\]

So, the slope of the line is \(m = \frac{1}{2}\).

### Step 2: Use the point-slope form to find the new line's equation
Since the required line is parallel to the given line, it has the same slope \(m = \frac{1}{2}\). Using the point-slope form of a line equation:

\[
y - y_1 = m(x - x_1)
\]

Where \((x_1, y_1) = (-2, 2)\) is the given point, we plug in the values:

\[
y - 2 = \frac{1}{2}(x + 2)
\]

Simplify the equation:
\[
y - 2 = \frac{1}{2}x + 1
\]
\[
y = \frac{1}{2}x + 3
\]

Thus, the equation of the line is:
\[
y = \frac{1}{2}x + 3
\]

Or in standard form:
\[
x - 2y + 6 = 0
\]

Would you like any further details or clarifications?

### Related Questions:
1. How do you find the slope of a line from an equation in standard form?
2. What is the relationship between parallel lines in terms of slope?
3. How do you convert from point-slope form to slope-intercept form?
4. How do you determine the equation of a line perpendicular to a given line?
5. What is the geometric interpretation of the slope of a line?

### Tip:
When working with parallel lines, remember that they always have identical slopes, which simplifies finding their equations!

Dapatkan persamaan garis yang melalui titik (-2, 2) dan selari dengan garis 2x - 4y - 8 = 0.

Discover how to find the equation of a line passing through the point (-2, 2) that is parallel to the line 2x - 4y - 8 = 0. Learn about linear equations, slopes, and point-slope form with this detailed step-by-step guide. Ideal for Grades 9-11 students.

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