We can rewrite the next equations in the slope-intercept form:
The first equation:
[tex]3x+4y=8\Rightarrow4y=8-3x\Rightarrow y=\frac{8}{4}-\frac{3}{4}x\Rightarrow y=2-\frac{3}{4}x\Rightarrow y=-\frac{3}{4}x+2[/tex]
The second equation:
[tex]6x+3y=6\Rightarrow3y=6-6x\Rightarrow y=\frac{6}{3}-\frac{6}{3}x\Rightarrow y=2-2x\Rightarrow y=-2x+2_{}[/tex]
As we can see, the slope of the first line is m = -3/4, and the slope of the second line is m = -2. Then, since the slope is different, these lines are not parallel (Option C).
