Question

the equation of line g is $y = \frac{3}{7}x + \frac{1}{6}$. 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 \( m_g \) and slope of line \( h \) is \( m_h \), then \( m_g \times m_h=-1 \).

Step2: Identify slope of line \( g \)

The equation of line \( g \) is in slope - intercept form \( y = mx + b \), where \( m \) is the slope. For \( y=\frac{3}{7}x+\frac{1}{6} \), the slope of line \( g \), \( m_g=\frac{3}{7} \).

Step3: Calculate slope of line \( h \)

Using the formula \( m_g\times m_h=-1 \), substitute \( m_g = \frac{3}{7} \):
\(\frac{3}{7}\times m_h=-1\)
To solve for \( m_h \), we can rewrite the equation as \( m_h=-1\div\frac{3}{7}\)
When dividing by a fraction, we multiply by its reciprocal, so \( m_h=-1\times\frac{7}{3}=-\frac{7}{3}\)

Answer:

\(-\frac{7}{3}\)