find the slope of a line perpendicular to the line whose equation is $x - 2y = 14$. fully simplify your…

Explanation:

Step1: Rewrite the given equation in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Starting with $x−2y = 14$, we solve for $y$: $-2y=-x + 14$, then $y=\frac{1}{2}x-7$. So the slope of the given line $m_1=\frac{1}{2}$.

Step2: Use the perpendicular slope formula

If two lines are perpendicular, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. We know $m_1 = \frac{1}{2}$, and substituting into $m_1\times m_2=-1$ gives $\frac{1}{2}\times m_2=-1$. Solving for $m_2$, we get $m_2=-2$.

Answer:

$-2$