Negative Slope
A negative slope means a line falls from left to right on a graph, indicating that as x increases, y decreases.
Formula
m < 0
Definition
A line has a negative slope when it falls from left to right, meaning $y$ decreases as $x$ increases; formally $m < 0$, and the more negative $m$ is, the steeper the decline (a slope of $-1$ creates a $45$-degree downward angle). This means $f(x) = mx + b$ is strictly decreasing on $\mathbb{R}$, with $f'(x) = m < 0$ everywhere, and the line makes an obtuse angle with the positive x-axis, $90^\circ < \theta < 180^\circ$, where $\tan\theta = m < 0$. Since perpendicular lines have slopes $m$ and $-1/m$, a line with negative slope always has a perpendicular with positive slope.
Example
$y = -3x + 6$ drops $3$ for every $1$ right, from $(0,6)$ to $(1,3)$. $y = -0.5x + 4$ declines gently (down $1$ per $2$ right), while $y = -5x + 10$ declines steeply (down $5$ per $1$ right). A slope of $m = -2$ gives $\theta = \arctan(-2) \approx 116.57^\circ$, and its perpendicular has slope $1/2$, with $(-2)(1/2) = -1$ confirming the perpendicularity.
Key Insight
A negative slope looks like a backslash \, like going down a hill as you walk right, and it signals an inverse relationship between variables: as temperature drops, heating costs rise; as speed increases on a fuel-limited trip, range decreases. A strictly decreasing linear function is also invertible, and its inverse has slope $1/m$ (also negative); note that $m \cdot (1/m) = 1$, not $-1$, so a line and its inverse (reflected over $y = x$) are generally not perpendicular to each other.