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.The equation of the given line is . We can rewrite this equation in slope-intercept form, which is , where is the slope and is the y-intercept.To do this, we can subtract from both sides of the equation to isolate : From this equation, we can see that the slope of the given line is .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.The negative reciprocal of is , which simplifies to .Therefore, the slope of a line perpendicular to the given line is .