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The problem asks for the equation of a line parallel to \( y = -x + 5 \) that passes through the point \( (8, -6) \).

Since parallel lines have the same slope, the slope of the new line will also be \( -1 \) (since the slope of \( y = -x + 5 \) is \( -1 \)).

Using the point-slope form equation \( y - y_1 = m(x - x_1) \) where \( m \) is the slope and \( (x_1, y_1) \) is the given point:

\[
y - (-6) = -1(x - 8)
\]

Simplifying:

\[
y + 6 = -1(x - 8)
\]

The correct equation is \( y + 6 = -(x - 8) \), which matches the last option.

So, the answer is: **\( y + 6 = -(x - 8) \)**.

Find the equation of a line parallel to y = -x + 5 that passes through the point (8, -6).

Learn how to find the equation of a line parallel to y = -x + 5 that passes through the point (8, -6). This problem covers concepts like algebra, linear equations, and the properties of parallel lines. Suitable for students in Grades 8-10.

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