Which Slope is larger?

Question

If a line has $\tan(120^\circ)$ as gradient or slope and another line has $\tan(130^\circ) $as slope, which slope is larger? I mean numerically $\tan(120^\circ)=-1.7320$ and $\tan(130^\circ)=-1.1917$. Since $-1.1917>-1.7320$ so this slope seems grater to me. But the steepness of slope $\tan(120^\circ)$ is higher. So which slope is larger?

Answer 1

Without additional context or information, the first argument seems to be correct. Since $\tan(120^\circ) < \tan(130^\circ)$, the second slope is larger.

Answer 2

The steepness of the slope is the absolute value of the gradient. $y=-10x$ looks steeper than $y=x$ even though $-10 < 1$.

Answer 3

In mathematics, we will investiget the slope, or gradient, or the angle of inclination of a line. There is no definition on the term "steepness".