Question

the equation of line c is $y = \frac{-9}{4}x + 8$. line d is perpendicular to c. what is the slope of line d? 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 with slopes \(m_1\) and \(m_2\), the product is \(-1\), i.e., \(m_1\times m_2=-1\).
The slope of line \(c\) (from \(y = \frac{-9}{4}x + 8\)) is \(m_1=\frac{-9}{4}\).

Step2: Solve for slope of line \(d\) (\(m_2\))

Using \(m_1\times m_2=-1\), substitute \(m_1 = \frac{-9}{4}\):
\(\frac{-9}{4}\times m_2=-1\)
Multiply both sides by \(\frac{4}{-9}\):
\(m_2=-1\times\frac{4}{-9}=\frac{4}{9}\)

Answer:

\(\frac{4}{9}\)