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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

Sagot :

Naǫidn
Convert all the equations to slope-intercept form:

[tex]\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}[/tex]

[tex]C. \\ y-2x=3 \ \ \ |+2x \\ y=2x+3 \\ \\ D. \\ -2y-4x=3 \ \ \ |+4x \\ -2y=4x+3 \ \ \ \|\div (-2) \\ y=-2x-\frac{3}{2}[/tex]

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.
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