Chapter 2 - Functions, Equations, and Graphs - 2-6 Families of Functions - Practice and Problem-Solving Exercises - Page 104: 29

$y=\dfrac{1}{4}x$

Recall: When $0\lt a \lt 1$, the graph of $y = a\cdot f(x)$ involves a vertical compression by a factor of $a$ of the graph of the parent function $f(x)$. Thus, when the graph of $y=x$ is compressed vertically by a factor of $\frac{1}{4}$, the equation of the new function is: $$y=\frac{1}{4}x$$