find the slope of a line perpendicular to the line whose equation is 3x + y = 8. fully simplify your answer.

Explanation:

Step1: Rewrite in slope - intercept form

Rewrite $3x + y=8$ as $y=-3x + 8$. The slope of this line $m_1=-3$.

Step2: Use perpendicular slope formula

The slope of a line perpendicular to a line with slope $m_1$ is $m_2=-\frac{1}{m_1}$. Substitute $m_1 = - 3$ into the formula: $m_2=-\frac{1}{-3}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$