Answer:
[tex]\large\boxed{D.\ y=-\dfrac{1}{2}x+7}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\k:\ A_1x+B_1=C_1\\\\l:\ A_2x+B_2y=C_2\\\\\text{then}\\\\k\ \parallel\ l\iff A_1=A_2\ \wedge\ B_1=B_2\\==========================[/tex]
[tex]\text{We have the equation:}\ 2x+4y=6\\\\\text{Therefore the equation of a parallel line is:}\ 2x+4y=C\\\\\text{Put the coordinates of the given point to the equation and solve for}\ C:\\\\(6,\ 4)\to x=6,\ y=4\\\\C=2(6)+4(4)\\C=12+16\\C=28\\\\\text{The equation in the standard form:}\\\\2x+4y=28[/tex]
[tex]\text{Convert to the slope-intercept form}\ y=mx+b:\\\\2x+4y=28\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\4y=-2x+28\qquad\text{divide both sides by 4}\\\\y=-\dfrac{2}{4}x+\dfrac{28}{4}\\\\y=-\dfrac{1}{2}x+7[/tex]
