find the slope of a line perpendicular to the line whose equation is 3x + 18y = 108. fully simplify your…

Explanation:

Step1: Rewrite the given line in slope - intercept form

First, solve the equation $3x + 18y=108$ for $y$. $18y=-3x + 108$, then $y=-\frac{3}{18}x+\frac{108}{18}$, which simplifies to $y =-\frac{1}{6}x + 6$. The slope of this line, $m_1=-\frac{1}{6}$.

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. Substitute $m_1 =-\frac{1}{6}$ into the equation: $-\frac{1}{6}\times m_2=-1$. Solve for $m_2$: $m_2 = 6$.

Answer:

$6$