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The given problem asks for the equation of a line that passes through the point \((1, 6)\) and is parallel to the line \(2x + y = 3\).

### Step 1: Find the slope of the given line.
We can rewrite the given line \(2x + y = 3\) in slope-intercept form \(y = mx + b\), where \(m\) is the slope.

\[
2x + y = 3 \implies y = -2x + 3
\]

The slope \(m\) of the line is \(-2\). 

### Step 2: Use the slope-point form to find the equation of the new line.
Since the line we're looking for is parallel to \(2x + y = 3\), it will have the same slope of \(-2\). Using the point-slope form of a line equation:

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

Substituting the slope \(m = -2\) and the point \((x_1, y_1) = (1, 6)\):

\[
y - 6 = -2(x - 1)
\]

Simplifying:

\[
y - 6 = -2x + 2
\]
\[
y = -2x + 8
\]

### Step 3: Convert back to standard form.
We can rearrange the equation \(y = -2x + 8\) to standard form by moving all terms to one side:

\[
2x - y = 8
\]

### Conclusion:
The correct equation is \(2x - y = 8\), which corresponds to option **C**.

Would you like further details or have any questions? Here are 5 related questions:

1. How do you determine the slope of a line from its equation?
2. How do you find the equation of a line passing through two points?
3. What changes in the equation of a line if it's perpendicular instead of parallel to another line?
4. How can you convert between point-slope and slope-intercept forms?
5. How do you determine the y-intercept of a line given its slope and a point?

**Tip:** The slope of parallel lines is always equal, while perpendicular lines have slopes that are negative reciprocals of each other.

Which equation describes the line that passes through the point (1, 6) and is parallel to the line 2x + y = 3?

Learn how to find the equation of a line that passes through the point (1, 6) and is parallel to the line 2x + y = 3. This problem covers key algebraic concepts, including linear equations and slopes. Suitable for students in Grades 8-10.

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