Answer
$ y-0=\displaystyle \frac{1}{4}(x-0) \qquad$ ... point-slope form
$ y=\displaystyle \frac{1}{4}x \qquad$ ... slope-intercept form
$f(x)=\displaystyle \frac{1}{4}x$ $\qquad$ ... function notation
Work Step by Step
Given: $m=\displaystyle \frac{1}{4}, \; (x_{1},y_{1})=(0,0)$
Point-slope form:
$y-y_{1}=m(x-x_{1})$
$ y-0=\displaystyle \frac{1}{4}(x-0) \qquad$ ... point-slope form
... Simplify to slope-intercept form, $ y=mx+b$
$ y=\displaystyle \frac{1}{4}x \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
