Question

consider the line $y = \frac{2}{5}x - \frac{2}{5}$. 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: \boxed{} slope of a perpendicular line: \boxed{}

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have the same slope. The given line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope. For the line \(y=\frac{2}{5}x-\frac{2}{5}\), the slope \(m=\frac{2}{5}\). So, the slope of a line parallel to this line is also \(\frac{2}{5}\).

Step2: Recall slope of perpendicular lines

The slope of a line perpendicular to a line with slope \(m\) is the negative reciprocal, i.e., \(m_{\perp}=-\frac{1}{m}\). Here, \(m = \frac{2}{5}\), so the negative reciprocal is \(-\frac{5}{2}\).

Answer:

Slope of a parallel line: \(\frac{2}{5}\)
Slope of a perpendicular line: \(-\frac{5}{2}\)