The general equation of a line is y=mx+c, where m is the slope and c is the y intercept.
Transform the equation of line -4x-2y=-6 into the general form.
[tex]\begin{gathered} -4x-2y=-6 \\ -2y=-6+4x \\ y=\frac{-1}{2}(-6+4x) \\ y=3-2x \\ y=-2x+3 \end{gathered}[/tex]Compare equation y=-2x+3 with y=mx+c. Then, we get
Slope, m=-2.
The slope of two parallel lines are equal. Therefore, the slope of a line parallel to -4x-2y=-6 is -2.
If m is the slope of line, then the slope of a line perpendicular to it is -1/m. Therefore, the slope of perpendicular line can be calculated as
[tex]\text{slope}=-\frac{1}{m}=-\frac{1}{(-2)}=\frac{1}{2}[/tex]Hence, the slope of perpendicular line is 1/2.
