Question

what is the slope of a line that is perpendicular to the line $y = \frac{1}{6}x + 4$? the slope of the line is \boxed{}

Explanation:

Step1: Recall slope of perpendicular lines

For two perpendicular lines with slopes \(m_1\) and \(m_2\), the product is \(-1\), i.e., \(m_1\times m_2=-1\).

Step2: Find slope of given line

The given line is \(y = \frac{1}{6}x + 4\), in slope - intercept form \(y=mx + b\) (where \(m\) is the slope), so the slope of the given line \(m_1=\frac{1}{6}\).

Step3: Calculate slope of perpendicular line

Let the slope of the perpendicular line be \(m_2\). Using \(m_1\times m_2=-1\), substitute \(m_1 = \frac{1}{6}\):
\(\frac{1}{6}\times m_2=-1\)
Multiply both sides by 6: \(m_2=-6\)

Answer:

\(-6\)