Question

any line perpendicular to the line shown has a slope equal to

Explanation:

Step1: Find the slope of the given line

Let two points on the line be $(- 6,0)$ and $(6,-6)$. Using the slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_1=\frac{-6 - 0}{6-(-6)}=\frac{-6}{12}=-\frac{1}{2}$.

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. Given $m_1 =-\frac{1}{2}$, then $-\frac{1}{2}\times m_2=-1$. Solving for $m_2$, we get $m_2 = 2$.

Answer:

$2$