Question

Which equation represents a line that intersects the line 2y − 4x = 3? A.-2y + 4x = 1 B. 3y − 6x = 6.5 C. y − 2x = 3 D. -2y − 4x = 3 Please help i can't miss this!

Answer 1

Convert all the equations to slope-intercept form:
$2y-4x=3 \ \ \ |+4x \\ 2y=4x+3 \ \ \ |\div 2 \\ y=2x+\frac{3}{2}$

$A. \\ -2y+4x=1 \ \ \ |-4x \\ -2y=-4x+1 \ \ \ |\div (-2) \\ y=2x-\frac{1}{2} \\ \\ B. \\ 3y-6x=6.5 \ \ \ |+6x \\ 3y=6x+6.5 \ \ \ |\div 3 \\ y=2x+\frac{13}{6}$

$C. \\ y-2x=3 \ \ \ |+2x \\ y=2x+3 \\ \\ D. \\ -2y-4x=3 \ \ \ |+4x \\ -2y=4x+3 \ \ \ |\div (-2) \\ y=-2x-\frac{3}{2}$

Lines A, B and C have the same slope as the line 2y-4x=3, so they are parallel and don't intersect it.
Line D has another slope, so it intersects the line 2y-4x=3.
The answer is D.