Determine whether the two lines below are parallel, perpendicular or neither.
\[
\begin{array}{l}
-x+y=14 \\
3 x+3 y=2
\end{array}
\]
parallel
perpendicular
neither
Since the lines are neither parallel nor perpendicular, the final answer is \(\boxed{\text{neither parallel nor perpendicular}}\)
Step 1 :Given two lines: \(-x+y=14\) and \(3x+3y=2\)
Step 2 :Rewrite the equations in slope-intercept form (y = mx + b), where m is the slope.
Step 3 :The first equation becomes \(y = x + 14\), so the slope (m1) is 1.
Step 4 :The second equation becomes \(y = -x + \frac{2}{3}\), so the slope (m2) is -1.
Step 5 :Compare the slopes. If the slopes are equal, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular.
Step 6 :The slopes are not equal (1 \neq -1), so the lines are not parallel.
Step 7 :The product of the slopes is not -1 (1 * -1 \neq -1), so the lines are not perpendicular.
Step 8 :Since the lines are neither parallel nor perpendicular, the final answer is \(\boxed{\text{neither parallel nor perpendicular}}\)