Question

the equation of line c is y = -6x + 90. 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

If two lines are perpendicular, the product of their slopes is -1. Let the slope of line \( c \) be \( m_c \) and slope of line \( d \) be \( m_d \), then \( m_c \times m_d=-1 \).

Step2: Find slope of line \( c \)

The equation of line \( c \) is \( y = -6x + 90 \), 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 \( c \), \( m_c=-6 \).

Step3: Calculate slope of line \( d \)

Using the formula \( m_c\times m_d=-1 \), substitute \( m_c = - 6 \) into it:
\(-6\times m_d=-1\)
To solve for \( m_d \), divide both sides of the equation by - 6:
\(m_d=\frac{-1}{-6}=\frac{1}{6}\)

Answer:

\(\frac{1}{6}\)