Positive Slope
A positive slope means a line rises from left to right on a graph, indicating that as x increases, y also increases.
Formula
m > 0
Definition
A line has a positive slope when it rises from left to right, meaning $y$ increases as $x$ increases; formally, $m > 0$ in $y = mx + b$, and the larger $m$ is, the steeper the upward climb (horizontal lines, where $m = 0$, are not positive-slope lines). A positive slope means the linear function $f(x) = mx + b$ is strictly increasing on $\mathbb{R}$, with $f'(x) = m > 0$ everywhere, and the angle $\theta$ the line makes with the positive x-axis satisfies $0 < \theta < 90^\circ$, with $\tan\theta = m$.
Example
$y = 2x + 1$ has slope $2$: starting at $(0,1)$, move right $1$ and up $2$ to reach $(1,3)$. $y = 0.5x - 3$ has a gentle positive slope (up $1$ for every $2$ right), while $y = 10x$ is very steep; both climb left to right. A slope of $m = 1$ gives $\theta = 45^\circ$, and $m = \sqrt{3}$ gives $\theta = 60^\circ$; as $m$ grows toward infinity the line approaches vertical.
Key Insight
A positive slope looks like a forward slash /, like climbing a hill as you walk to the right. In data, it signals a positive correlation, as one quantity grows, so does the other, as with height versus shoe size or hours studied versus test score. Because it corresponds to a strictly (monotone) increasing function, positive slope is also exactly the condition for a linear function to be invertible over its whole domain.