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

Explanation:

Step1: Recall slope - perpendicular line rule

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$.

Step2: Identify the slope of the given line

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

Step3: Calculate the slope of the perpendicular line

Let the slope of the perpendicular line be $m_2$. We know that $m_1\times m_2=-1$. Substituting $m_1 = \frac{1}{6}$ into the equation $\frac{1}{6}\times m_2=-1$. Solving for $m_2$, we get $m_2=-6$ by multiplying both sides of the equation by $6$.

Answer:

$-6$