Question

Which equation represents a line which is parallel to the line y=8x-4?A x+8y=-16B x-8y=-40C y-8x=-1D 8x+y=3

Answer 1

Two parallel lines has the same slope.

The given line:

`y=8x-4`

Is written in the form y=mx+b where m is the slope.

The slope is 8

To find the parallel line you need to write the given options in the form y=mx+b by solving y, as follow:

`\begin{gathered} A \\ x+8y=-16 \\ 8y=-x-16 \\ y=-(1)/(8)x-(16)/(8) \\ \\ y=-(1)/(8)x-2 \end{gathered}`

Slope is -1/8 (it is not parallel to given line)

_______________

`\begin{gathered} B \\ x-8y=-40 \\ -8y=-x-40 \\ y=(-x)/(-8)-(40)/(-8) \\ \\ y=(1)/(8)x+5 \end{gathered}`

Slope is 1/8 (it is not parallel to given line)

________________

`\begin{gathered} C \\ y-8x=-1 \\ y=8x-1 \end{gathered}`

Slope is 8 (It is parallel to given line)

___________

`\begin{gathered} D \\ 8x+y=3 \\ y=-8x+3 \end{gathered}`

Slope is -8 (it is not parallel to given line)

Then, as given line and line in option C have the same slope (8) they are parallel lines