Question

4) Is each line parallel, perpendicular, or neither to the line - 4x + 5y = 20.Show ALL of your work; be sure to show the slope for the given equation and the slope for eachline below. -x+5y =157x + 3y =-18- 3x + 7y = 147x-3y=5

Answer 1

We have the following:

We must pass each equation to the following form:

`y=mx+b`

where m is the slope

when two lines are parallel the slopes are equal, when they are perpendicular they are inverse

therefore,

`\begin{gathered} -4x+5y=20 \\ 5y=4x+20 \\ y=(4)/(5)x+4 \end{gathered}`

The slope is 4/5, the inverse is -5/4

now, for:

`\begin{gathered} -x+5y=15 \\ 5y=x+15 \\ y=(1)/(5)x+3 \end{gathered}`

therefore, they are neither parallel nor perpendicular

`\begin{gathered} 7x+3y=-18 \\ 3y=-7x+18 \\ y=-(7)/(3)x+6 \end{gathered}`

therefore, they are neither parallel nor perpendicular

`\begin{gathered} -3x+7y=14 \\ 7y=3x+14 \\ y=(3)/(7)x+2 \end{gathered}`

therefore, they are neither parallel nor perpendicular

`\begin{gathered} 7x-3y=5 \\ 3y=7x-5 \\ y=(7)/(3)x-(5)/(3) \end{gathered}`

therefore, they are neither parallel nor perpendicular

7x + 3y =-18 and - 3x + 7y = 14 are perpendicular