Rewrite equation 4x + 2y = 6 into the form y=mx+c, where m is the slope and c is the y intercept.
[tex]\begin{gathered} 2y=-4x+6 \\ y=\frac{-4x}{2}+\frac{6}{2} \\ y=-2x+3\text{ ---(1)} \end{gathered}[/tex]Comparing equation (1) with y=mx+c, we get m=-2.
Hence, the slope of the line 4x + 2y = 6 is m=-2
So, the slope of a line perpendicular to 4x + 2y = 6 is,
[tex]\begin{gathered} M=\frac{-1}{m} \\ M=\frac{-1}{-2} \\ =\frac{1}{2} \end{gathered}[/tex]Therefore, the the slope of a line perpendicular to 4x + 2y = 6 is M=1/2.
Now, rewrite th equation 2x+y=-2 into the form y=mx+c.
[tex]y=-2x-2\text{ ---(2)}[/tex]Comparing equation (2) with y=mx+c, the y intercept of line 2x+y=-2 is c=-2.
Now, the equation of a line with slope M=1/2 and y intercept c=-2 is given by,
[tex]\begin{gathered} y=Mx+c \\ y=\frac{1}{2}x-2 \end{gathered}[/tex]Therefore, the equation of a line perpendicular to the line 4x + 2y = 6 having the same y-intercept as 2x + y = -2 is,
[tex]y=\frac{1}{2}x-2[/tex]