Question

Rewrite each equation in slope intercept form, if necessary. Then determine whether the lines are parallel. Explain3x+4y = 86x+3y = 6Are these lines parallel?A.B.C.D.(look at image for answer choices)

Answer 1

We can rewrite the next equations in the slope-intercept form:

The first equation:

`3x+4y=8\Rightarrow4y=8-3x\Rightarrow y=(8)/(4)-(3)/(4)x\Rightarrow y=2-(3)/(4)x\Rightarrow y=-(3)/(4)x+2`

The second equation:

`6x+3y=6\Rightarrow3y=6-6x\Rightarrow y=(6)/(3)-(6)/(3)x\Rightarrow y=2-2x\Rightarrow y=-2x+2_{}`

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).