Question

Determine if the lines are parallel, perpendicular, or neither Line 1: 7x=2y-16Line 2: 10y=35x-70

Answer 1

Okay, here we have this:

Considering the provided equations, that parallel lines have the same slope and the multiplication of the slopes of the perpendicular lines is -1, we are going to calculate the slope of each line, so we obtain the following:

Line 1:

`\begin{gathered} 7x=2y-16 \\ 2y=7x+16 \\ y=(7)/(2)x+8 \end{gathered}`

And, as the form of the equation is y=mx+b, where m is the slope, replacing in this case we obtain that the slope 7/2.

Line 2:

`\begin{gathered} 10y=35x-70 \\ y=(35)/(10)x-(70)/(10) \\ y=(7)/(2)x-7 \end{gathered}`

Here, we obtain that the slope is also 7/2.

Finally we obtain that the slopes are equal, so this mean that the lines are parallel.