Answer
$ y=2x-\dfrac{3}{2} $
(See graph below)
Work Step by Step
Using the properties of equality, the Slope-Intercept Form ($y=mx+b$) of the given equation, $
4x-2y=3
,$ is \begin{align*}\require{cancel} -2y&=-4x+3 \\\\ \dfrac{-2y}{-2}&=\dfrac{-4x+3}{-2} \\\\ y&=\dfrac{-4}{-2}x+\dfrac{3}{-2} \\\\ y&=2x-\dfrac{3}{2} .\end{align*}
To graph the given equation, use the intercepts.
If $y=0,$ then
\begin{align*}
4x-2(0)&=3
\\
4x&=3
\\\\
\dfrac{4x}{4}&=\dfrac{3}{4}
\\\\
x&=\dfrac{3}{4}
.\end{align*}
The $x$-intercept is $
\left(\dfrac{3}{4},0\right)
$.
If $x=0,$ then
\begin{align*}
4(0)-2y&=3
\\
-2y&=3
\\\\
\dfrac{-2y}{-2}&=\dfrac{3}{-2}
\\\\
y&=-\dfrac{3}{2}
.\end{align*}
The $y$-intercept is $
\left( 0,-\dfrac{3}{2}\right)
$.
Connecting the intercepts with a line, the graph of the given equation is shown above.
