Answer
The linear function whose graph has the slope $18$ and $y\text{-intercept }\left( 0,\frac{1}{2} \right)$ is$y=18x+\frac{1}{2}$.
Work Step by Step
Using the slope intercept form equation, we substitute $18$ for $m$ and $\frac{1}{2}$ for $b$:
$y=18x+\frac{1}{2}$