Find the slope of a line perpendicular to the line whose equation is x+y=9 Fully simplify your answer.

To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line.<br /><br />The equation of the given line is $x+y=9$. We can rewrite this equation in slope-intercept form, which is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.<br /><br />To do this, we can subtract $x$ from both sides of the equation to isolate $y$:<br /><br />$y=-x+9$<br /><br />From this equation, we can see that the slope of the given line is $-1$.<br /><br />Now, to find the slope of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.<br /><br />The negative reciprocal of $-1$ is $\frac{1}{1}$, which simplifies to $1$.<br /><br />Therefore, the slope of a line perpendicular to the given line is $\boxed{1}$.