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The question asks for the equation of a line that passes through the point \((6, -8)\) and is parallel to the line \(x + 2y = 6\).

### Step 1: Find the slope of the given line
We start with the equation of the given line \(x + 2y = 6\). First, convert it to slope-intercept form \(y = mx + b\) to find the slope.

\[
x + 2y = 6
\]
Subtract \(x\) from both sides:
\[
2y = -x + 6
\]
Now divide by 2:
\[
y = -\frac{1}{2}x + 3
\]

The slope \(m\) of this line is \(-\frac{1}{2}\).

### Step 2: Use the slope of the parallel line
Since parallel lines have the same slope, the slope of the new line is also \(-\frac{1}{2}\).

### Step 3: Use the point-slope form
The equation of a line with slope \(m\) passing through a point \((x_1, y_1)\) is given by:
\[
y - y_1 = m(x - x_1)
\]
Here, \(m = -\frac{1}{2}\), \(x_1 = 6\), and \(y_1 = -8\). Substituting into the point-slope form:

\[
y - (-8) = -\frac{1}{2}(x - 6)
\]
Simplifying:
\[
y + 8 = -\frac{1}{2}(x - 6)
\]
Distribute the \(-\frac{1}{2}\):
\[
y + 8 = -\frac{1}{2}x + 3
\]
Now subtract 8 from both sides to solve for \(y\):
\[
y = -\frac{1}{2}x + 3 - 8
\]
\[
y = -\frac{1}{2}x - 5
\]

### Final Equation:
The equation of the line is:
\[
y = -\frac{1}{2}x - 5
\]

Let me know if you need further clarification, or if you'd like to explore more examples!

### 5 Related Questions:
1. How do you find the equation of a line perpendicular to a given line?
2. What is the slope of a vertical line?
3. How can you convert an equation from slope-intercept form to standard form?
4. What is the significance of the y-intercept in the equation of a line?
5. How do parallel lines behave in a coordinate plane?

### Tip:
Always convert equations to slope-intercept form to easily compare slopes for parallel or perpendicular relationships.

What is an equation of the line that passes through the point (6, -8) and is parallel to the line x + 2y = 6?

Learn how to find the equation of a line parallel to x + 2y = 6 that passes through the point (6, -8). This step-by-step solution covers linear equations, slope-intercept form, and the point-slope form. Suitable for students in Grades 9-11.

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