Question

question
find the slope of a line perpendicular to the line whose equation is ( x - 3y = 27 ). fully simplify your ans

Explanation:

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

Start with the equation $x - 3y=27$. We want to solve for $y$.
Subtract $x$ from both sides: $- 3y=-x + 27$.
Divide each term by $-3$: $y=\frac{-x}{-3}+\frac{27}{-3}$, which simplifies to $y=\frac{1}{3}x - 9$.
So the slope of the given line, $m_1$, is $\frac{1}{3}$.

Step2: Find the slope of the perpendicular line.

The slope of a line perpendicular to a line with slope $m$ is the negative reciprocal of $m$. That is, if the slope of one line is $m_1$, the slope of the line perpendicular to it, $m_2$, is given by $m_2=-\frac{1}{m_1}$.
Since $m_1 = \frac{1}{3}$, then $m_2=-\frac{1}{\frac{1}{3}}=-3$.

Answer:

The slope of the line perpendicular to the given line is $-3$.