Question

find the slope of a line perpendicular to the line whose equation is $3x - 3y = 45$. 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 $3x - 3y=45$. First, we want to solve for $y$. Subtract $3x$ from both sides:
$-3y=-3x + 45$
Then divide each term by $-3$:
$y=\frac{-3x}{-3}+\frac{45}{-3}$
$y = x-15$
The slope of the given line ($m_1$) is $1$ (since in $y = mx + b$, $m = 1$ here).

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 $m_2$. Then we have the equation:
$m_1\times m_2=-1$
We know that $m_1 = 1$, so substitute it into the equation:
$1\times m_2=-1$
So $m_2=-1$.

Answer:

$-1$