Answer
The steepness when $m>0$ is greater as $m$ increases.
The steepness when $m<0$ is greater as $m$ decreases.
Work Step by Step
Graph the equation $y=mx$ for $m=-3,-2,-1,1,2,3$.
We notice that the lines with $m>0$ lie in Quadrants I and III; when $m$ grows, the steepness grows, and the line gets closer and closer to the $y$-axis.
When $m<0$, the lines lie in Quadrants II and IV; when $m$ decreases, the steepness grows, and the line gets closer and closer to the $y$-axis.