To find the slope of a line parallel to the line given by the equation \(2x - 6y = -1\), we first need to rewrite this equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope.
Starting with the equation:
\[2x - 6y = -1\]
We can isolate \(y\):
- Subtract \(2x\) from both sides:
\[-6y = -2x - 1\]
- Now, divide every term by \(-6\):
\[y = \frac{2}{6}x + \frac{1}{6}\]
- Simplifying the fractions gives:
\[y = \frac{1}{3}x + \frac{1}{6}\]
From this, we can see that the slope \(m\) of the line is \(\frac{1}{3}\).
Lines that are parallel to each other have the same slope. Therefore, the slope of any line parallel to the line defined by \(2x - 6y = -1\) is also:
\[\frac{1}{3}\]