Question

which of the following represents a line that is parallel to the line with equation y = – 3x + 4 ?A. 6x +2y = 15B. 3x - y = 7 C. 2x - 3y = 6D. x + 3y = 1

Answer 1

In order to have parallel lines, the slopes of the lines need to be the same.

In order to check the slope for each option, let's put the equations in the slope-intercept form:

`y=mx+b`

Where m is the slope and b is the y-intercept.

So we have that:

A.

`\begin{gathered} 6x+2y=15 \\ 2y=-6x+15 \\ y=-3x+7.5 \end{gathered}`

B.

`\begin{gathered} 3x-y=7 \\ y=3x-7 \end{gathered}`

C.

`\begin{gathered} 2x-3y=6 \\ 3y=2x-6 \\ y=(2)/(3)x-2 \end{gathered}`

D.

`\begin{gathered} x+3y=1 \\ 3y=-x+1 \\ y=-(1)/(3)x+(1)/(3) \end{gathered}`

So the only option with a line with a slope of -3 is Option A.