Consider the line \( y=\frac{1}{4} x \) What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: Slope of a perpendicular line:

The slope of a parallel line is the same as the slope of the original line, which is \( \frac{1}{4} \). So, any line parallel to \( y = \frac{1}{4}x \) will also rise one unit for every four units it runs to the right. On the flip side, the slope of a perpendicular line can be found using the negative reciprocal of the original slope. Since the slope of the given line is \( \frac{1}{4} \), the negative reciprocal would be \( -4 \). Thus, a line perpendicular to \( y = \frac{1}{4}x \) will steeply fall, descending four units for every unit it runs to the right!