Question

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

Answer 1

To find the slope of a line that is perpendicular to the line given by the equation \(x + y = 9\), we first need to determine the slope of the given line.

1. **Rearrange the equation** into slope-intercept form \(y = mx + b\), where \(m\) is the slope:
\[
x + y = 9
\]
Subtract \(x\) from both sides:
\[
y = -x + 9
\]
From this, we can see that the slope \(m\) of the line is \(-1\).

2. **Find the slope of the perpendicular line**. The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. The negative reciprocal of \(-1\) is:
\[
\text{Perpendicular slope} = -\frac{1}{-1} = 1
\]

Thus, the slope of a line perpendicular to the line whose equation is \(x + y = 9\) is \(\boxed{1}\).