Question

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

Explanation:

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

We start with the equation $x - y=3$. To solve for $y$, we can subtract $x$ from both sides:
$-y=-x + 3$
Then multiply both sides by $- 1$ to get $y=x - 3$. In the slope - intercept form $y = mx + b$, the slope $m$ of the given line is $1$.

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line. Let the slope of the given line be $m_1$ and the slope of the perpendicular line be $m_2$. The formula for the slope of a perpendicular line is $m_2=-\frac{1}{m_1}$.
Since $m_1 = 1$, then $m_2=-\frac{1}{1}=-1$.

Answer:

$-1$