Question

find the slope of a line perpendicular to the line whose equation is ( x + y = 9 ). fully simplify your answer.

Explanation:

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

The equation of the given line is $x + y = 9$. We can rewrite it as $y=-x + 9$. 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 product of their slopes is $-1$. Let the slope of the perpendicular line be $m_{perp}$. We know that $m\times m_{perp}=-1$. Since $m=-1$, we substitute it into the equation: $-1\times m_{perp}=-1$. Solving for $m_{perp}$, we divide both sides of the equation by $-1$: $m_{perp}=\frac{-1}{-1}=1$.

Answer:

The slope of the line perpendicular to the line $x + y = 9$ is $1$.