Question

consider the line $y = \frac{2}{3}x$. 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: \boxed{} slope of a perpendicular line: \boxed{}

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = \frac{2}{3}x \), which is in slope - intercept form \( y=mx + b \) where \( m \) is the slope. So the slope of the given line is \( \frac{2}{3} \). A line parallel to it will have the same slope.

Step2: Recall slope of perpendicular lines

The slope of a line perpendicular to a line with slope \( m \) is the negative reciprocal of \( m \). If \( m=\frac{2}{3} \), the negative reciprocal is \( -\frac{3}{2} \) (we flip the fraction \( \frac{2}{3} \) to get \( \frac{3}{2} \) and then change the sign).

Answer:

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