1. The problem asks to compare the steepness of the lines $g(x) = \frac{1}{3}x$ and $f(x) = x$. 2. The steepness of a line is determined by the absolute value of its slope. 3. The slope of $f(x)$ is $1$. 4. The slope of $g(x)$ is $\frac{1}{3}$. 5. Since $\left|1\right| > \left|\frac{1}{3}\right|$, the line $f(x)$ is steeper than $g(x)$. 6. Therefore, $g(x) = \frac{1}{3}x$ is less steep than $f(x) = x$. Final answer: $g(x)$ is less steep than $f(x)$.