find the slope of a line perpendicular to the line whose equation is 6x + y = -5. fully simplify your answer.

Explanation:

Step1: Rewrite the given equation in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Given $6x + y=-5$, we can rewrite it as $y=-6x - 5$. So the slope of the given line, $m_1=-6$.

Step2: Use the perpendicular slope formula

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=-1$. We know $m_1 = - 6$, and we want to find $m_2$. Substituting into the formula $-6\times m_2=-1$. Solving for $m_2$, we get $m_2=\frac{1}{6}$.

Answer:

$\frac{1}{6}$