The inequality \(y \geq -x\) represents a half-plane where \(y\) is greater than or equal to the negation of \(x\). The line's slope (\(m\)) is -1, indicating a downward-sloping line.
The inequality \(y \geq -x\) represents a half-plane where \(y\) is greater than or equal to the negation of \(x\). To determine the slope (\(m\)) of the line that represents this inequality in slope-intercept form (\(y = mx + b\)), you can rewrite the inequality in the form \(y = mx + b\).
For \(y \geq -x\), add \(x\) to both sides:
\[ y + x \geq 0 \]
Now, subtract \(x\) from both sides:
\[ y \geq -x \]
This is in the form \(y \geq mx\), where \(m = -1\). Therefore, the slope \(m\) is -1 for the inequality \(y \geq -x\).