Question

the equation of line g is $y = \frac{-9}{2}x + \frac{5}{2}$. line h is perpendicular to g. what is the slope of line h? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope of perpendicular lines

For two perpendicular lines, the product of their slopes is -1. If the slope of line \( g \) is \( m_1 \) and slope of line \( h \) is \( m_2 \), then \( m_1\times m_2=-1 \).
The equation of line \( g \) is in slope - intercept form \( y = m_1x + b \), where \( m_1=\frac{-9}{2} \).

Step2: Solve for \( m_2 \)

We know that \( m_1\times m_2=-1 \). Substitute \( m_1 = \frac{-9}{2} \) into the equation:
\(\frac{-9}{2}\times m_2=-1\)
To solve for \( m_2 \), we can multiply both sides of the equation by the reciprocal of \( \frac{-9}{2} \), which is \( \frac{-2}{9} \) (or we can use the formula \( m_2=\frac{-1}{m_1} \)).
Using \( m_2=\frac{-1}{m_1} \), substitute \( m_1 = \frac{-9}{2} \):
\( m_2=\frac{-1}{\frac{-9}{2}} \)
When dividing by a fraction, we multiply by its reciprocal, so \( m_2=-1\times\frac{2}{-9}=\frac{2}{9} \)

Answer:

\(\frac{2}{9}\)