Question

the equation of line ( j ) is ( y = \frac{-5}{6}x + 3 ). line ( k ) is perpendicular to ( j ). what is the slope of line ( k )? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall the slope of perpendicular lines

The slopes of two perpendicular lines are negative reciprocals of each other. That is, if the slope of one line is \( m \), the slope of the line perpendicular to it is \( -\frac{1}{m} \).

Step2: Identify the slope of line \( j \)

The equation of line \( j \) is \( y = \frac{-5}{6}x + 3 \). In the slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept), the slope of line \( j \), \( m_j=-\frac{5}{6} \).

Step3: Calculate the slope of line \( k \)

Since line \( k \) is perpendicular to line \( j \), let the slope of line \( k \) be \( m_k \). Then \( m_k=-\frac{1}{m_j} \). Substitute \( m_j = -\frac{5}{6} \) into the formula:
\( m_k=-\frac{1}{-\frac{5}{6}}=\frac{6}{5} \)

Answer:

\(\frac{6}{5}\)