We are to look for lines that are not parallel to y=3x + 4
Comparing the above equation with y=mx + b, the slope(m) = 3
Equations of lines are said to be parallel, if they have the same slope
So, we need to re-write each equation in the slope-intercept form to see which is NOT parallel to the given equation
OPTION A
3y - 9x - 6 = 0
[tex]y=\frac{9x}{3}+\frac{6}{3}[/tex][tex]y=3x+2[/tex]
slope = 3 which implies. it is parallel to the given equation
OPTION B
-2y + 6x + 4 = 0
[tex]2y=6x+4[/tex]
Divide through by 2
[tex]y=3x\text{ + 2}[/tex]
slope = 3 which implies the line is parallel to the given line
OPTION C
2y - 6x - 4 = 0
[tex]2y=6x\text{ + 4}[/tex]
Divide through the equation by 2
[tex]y=3x\text{ + 2}[/tex]
slope = 3 which implies the line is parallel to the given line
OPTION D
2y - 4x - 8 = 0
[tex]2y=4x\text{ + 8}[/tex]
Divide through the equation by 2
[tex]y=2x\text{ + 4}[/tex]
slope = 2, which means tthe line is NOT parallel to the given line.
Therefore, the line which is NOT parallel to y=3x+ 4 is D. 2y - 4x - 8 = 0
