Find the slope of a line parallel to the line whose equation is 3, x, plus, 18, y, equals, minus, 4863x+18y=−486. Fully simplify your answer.

1. Break Down the Problem

We need to find the slope of a line that is parallel to the given line. The given line is in the standard form $Ax + By = C$. We need to first convert this equation into slope-intercept form $y = mx + b$, where $m$ is the slope.

2. Relevant Concepts

For a line in the form $Ax + By = C$, the slope $m$ can be found by rearranging it into the form $y = mx + b$.

3. Analysis and Detail

Starting with the equation: $3x + 18y = -486$

We can isolate $y$:

1. Subtract $3x$ from both sides: $18y = -3x - 486$

2. Now, divide by $18$ to solve for $y$: $y = -\frac{3}{18}x - \frac{486}{18}$

3. Simplify the fractions: $y = -\frac{1}{6}x - 27$

From this equation, we can see that the slope $m$ of the line is $-\frac{1}{6}$.

4. Verify and Summarize

Since parallel lines have the same slope, the slope of any line parallel to our given line must also be $-\frac{1}{6}$.

Final Answer

The slope of a line parallel to the given line is $\mathbf{-\frac{1}{6}}$.