find the slope of a line perpendicular to the line whose equation is $x + 4y = 28$. 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. Given $x + 4y=28$, solve for $y$: $4y=-x + 28$, so $y=-\frac{1}{4}x+7$. The slope of this line, $m_1 =-\frac{1}{4}$.

Step2: Use the perpendicular - slope relationship

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$. Let the slope of the perpendicular line be $m_2$. We know $m_1 =-\frac{1}{4}$, so $-\frac{1}{4}\times m_2=-1$. Solve for $m_2$: $m_2 = 4$.

Answer:

$4$