Question

May you state whether the two lines are parallel, perpendicular or neither. y = 1/5x - 2; 5x + y = 3

Answer 1

Perpendicular.

Step-by-step explanation:

We will need to recall the basic definitions below:

• The slope-intercept form of the equation of a line is y=mx+b.

• Two lines are parallel if their slopes are the same.

,

• Two lines are perpendicular if the product of their slopes is -1.

Given the two lines:

`\begin{gathered} y=(1)/(5)x-2 \\ \implies\text{Slope}=(1)/(5) \end{gathered}`

The second line:

`\begin{gathered} 5x+y=3 \\ \implies y=-5x+4 \\ \implies\text{Slope}=-5 \end{gathered}`

The product of the slopes:

`\begin{gathered} =(1)/(5)*-5 \\ =-1 \end{gathered}`

Thus, the two lines are perpendicular.