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.