Convert all the equations to slope-intercept form:
\(\hbox{the given line:} \\ 2y-4x=3 \ \ \ |+4x \\
2y=4x+3 \ \ \ |\div 2 \\
y=2x+\frac{3}{2} \\ \\
A. \\
-2y+4x=1 \ \ \ |-4x \\
-2y=-4x+1 \ \ \ |\div (-2) \\
y=2x-\frac{1}{2} \\ \\
B. \\
3y-6x=6.5 \ \ \ |+6x \\
3y=6x+6.5 \ \ \ |\div 3 \\
y=2x+\frac{6.5}{3}\)
\(C. \\
y-2x=3 \ \ \ |+2x \\
y=2x+3 \\ \\
D. \\
-2y-4x=3 \ \ \ |+4x \\
-2y=4x+3 \ \ \ \|\div (-2) \\
y=-2x-\frac{3}{2}\)
If two lines have the same slope, they're parallel and don't intersect.
The slope of the given line is 2.
The slopes of lines A, B and C are also equal to 2, so they are all parallel.
The slope of line D is -2, so it intersects the given line.
The answer is D.
