find the slope of a line perpendicular to the line whose equation is 4x - 2y = 20. fully simplify your answer.

Explanation:

Step1: Rewrite the given equation in slope - intercept form

First, rewrite $4x - 2y=20$ as $y = mx + b$. Subtract $4x$ from both sides: $-2y=-4x + 20$. Divide by $-2$: $y = 2x-10$. The slope of this line, $m_1 = 2$.

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. We know $m_1 = 2$, so $2\times m_2=-1$. Solve for $m_2$: $m_2=-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$