Question

perpendicular line: your turn!
if a line has an equation of ( 2y = 3x + 3 ), what is the slope of a line that is perpendicular to the line?

a. ( -2 )
b. ( 3 )
c. ( \frac{3}{2} )
d. ( -\frac{2}{3} )
e. ( -\frac{3}{2} )

Explanation:

Step1: Find slope of given line

First, rewrite \(2y = 3x + 3\) in slope - intercept form \(y=mx + b\) (where \(m\) is the slope). Divide both sides by 2: \(y=\frac{3}{2}x+\frac{3}{2}\). So the slope of the given line \(m_1=\frac{3}{2}\).

Step2: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope \(m_1\) is \(m_2=-\frac{1}{m_1}\). Substitute \(m_1 = \frac{3}{2}\) into the formula: \(m_2=-\frac{1}{\frac{3}{2}}=-\frac{2}{3}\).

Answer:

d. \(-\frac{2}{3}\)