Question

question
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 ($y = mx + b$, where $m$ is the slope)

Start with the equation $4x - 2y=20$.
Subtract $4x$ from both sides: $- 2y=-4x + 20$.
Divide each term by $-2$: $y = 2x-10$.
So the slope of the given line ($m_1$) is $2$.

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of the perpendicular line be $m_2$.
We know that $m_1\times m_2=-1$.
Substitute $m_1 = 2$ into the equation: $2\times m_2=-1$.
Solve for $m_2$ by dividing both sides by $2$: $m_2=-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$