Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x+5}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 4x+2y=1.\ \text{Convert to the slope-intercept form y = mx + b:}\\\\4x+2y=1\qquad\text{subtract 4x from both sides}\\\\2y=-4x+1\qquad\text{divide both sides by 2}\\\\y=-2x+\dfrac{1}{2}\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{2}x+b.\\\\\text{The line passes through }(-4,\ 3).[/tex]
[tex]\text{Put the coordinates of the point to the equation.}\ x=-4,\ y=3:\\\\3=\dfrac{1}{2}(-4)+b\\\\3=-2+b\qquad\text{add 2 to both sides}\\\\b=5[/tex]
