Question

the equation of line q is $y = \frac{-2}{9}x + 2$. line r is perpendicular to q. what is the slope of line r? 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 \( q \) is \( m_q \) and the slope of line \( r \) is \( m_r \), then \( m_q \times m_r=-1 \).

Step2: Identify slope of line \( q \)

The equation of line \( q \) is in slope - intercept form \( y = mx + b \), where \( m \) is the slope. For \( y=\frac{-2}{9}x + 2 \), the slope of line \( q \), \( m_q=\frac{-2}{9} \).

Step3: Calculate slope of line \( r \)

Using the formula \( m_q\times m_r=-1 \), substitute \( m_q = \frac{-2}{9} \) into it:
\(\frac{-2}{9}\times m_r=-1\)
To solve for \( m_r \), we can multiply both sides of the equation by the reciprocal of \( \frac{-2}{9} \), which is \( \frac{-9}{2} \).
\( m_r=-1\times\frac{-9}{2}=\frac{9}{2} \)

Answer:

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