Question

the equation of line p is $y = \frac{-7}{8}x + 1$. line q is perpendicular to p. what is the slope of line q? 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. Let the slope of line \( p \) be \( m_p \) and slope of line \( q \) be \( m_q \), then \( m_p \times m_q=-1 \).

Step2: Identify slope of line \( p \)

The equation of line \( p \) is \( y = \frac{-7}{8}x + 1 \), which is in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept). So, the slope of line \( p \), \( m_p=\frac{-7}{8} \).

Step3: Calculate slope of line \( q \)

Using the formula \( m_p\times m_q=-1 \), substitute \( m_p = \frac{-7}{8} \) into it. We get \( \frac{-7}{8}\times m_q=-1 \). To solve for \( m_q \), we can rewrite the equation as \( m_q=\frac{-1}{\frac{-7}{8}} \). When dividing by a fraction, we multiply by its reciprocal, so \( m_q=-1\times\frac{8}{-7}=\frac{8}{7} \).

Answer:

\(\frac{8}{7}\)