Question

consider the line $y = \frac{1}{2}x$. 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:

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = \frac{1}{2}x \), which is in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept). Here, the slope \( m=\frac{1}{2} \). So, the slope of a line parallel to this line will also be \( \frac{1}{2} \).

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 \( m=\frac{1}{2} \), the negative reciprocal is \( - \frac{1}{\frac{1}{2}}=- 2 \).

Answer:

Slope of a parallel line: \(\frac{1}{2}\)
Slope of a perpendicular line: \(-2\)