Question

consider the line $y = \frac{2}{3}x$. what is the slope of a line perpendicular to this line? what is the slope of a line parallel to this line? slope of a perpendicular line: \boxed{} slope of a parallel line: \boxed{}

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = \frac{2}{3}x \), so its slope \( m = \frac{2}{3} \). Thus, the slope of a parallel line is also \( \frac{2}{3} \).

Step2: Recall slope of perpendicular lines

The slope of a line perpendicular to a line with slope \( m \) is the negative reciprocal, i.e., \( -\frac{1}{m} \). For \( m = \frac{2}{3} \), the negative reciprocal is \( -\frac{3}{2} \).

Answer:

Slope of a perpendicular line: \(-\frac{3}{2}\)
Slope of a parallel line: \(\frac{2}{3}\)