Question

find the slope of a line perpendicular to the line whose equation is ( x + 4y = 16 ). fully simplify your answer.

Explanation:

Step1: Rewrite the given equation in slope - intercept form ($y = mx + b$, where $m$ is the slope)

We start with the equation $x + 4y=16$.
Subtract $x$ from both sides: $4y=-x + 16$.
Then divide each term by 4: $y=-\frac{1}{4}x + 4$.
So the slope of the given line, $m_1$, is $-\frac{1}{4}$.

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 $m_1 = -\frac{1}{4}$ into the equation: $-\frac{1}{4}\times m_2=-1$.
To solve for $m_2$, multiply both sides of the equation by - 4: $m_2=(-1)\times(-4)=4$.

Answer:

4