How is the slope of a line related to speed?

$s = \frac{d}{t}$, where $s$ denotes speed, $d$, distance, and $t$, time
So, $d$ is a function of $t$, which can be written as: $d = s t$
We know that the general formula for the slope-intercept form is $y = m x + b$
We can easily notice that our function $d$ is in fact written in slope-intercept form, with the free term $b$ (intercept) being $0$:
$d = s t + 0$