Question

Consider the line y= -1/4x + 2.What is the slope of a line parallel to this line?What is the slope of a line perpendicular to this line?

Answer 1

Given:

The given equation of a line is,

`y=-(1)/(4)x+2`

The objective is to find the slope of a parallel line and the slope of a perpendicular line.

Step-by-step explanation:

The general equation of a straight line is,

`y=mx+b`

Here, m represents the slope of the equation.

By comparing the general equation with the given equation,

`m=-(1)/(4)`

To find slope of parallel lines:

The slope value of two parallel lines will always be equal.

`\text{Slope of parallel line =-}(1)/(4)`

To find slope of perpendicular line:

But for perpendicular lines the product of slope value of two perpendicular lines will be (-1).

`\begin{gathered} m*\text{Slope of perpendicular line = -1} \\ -(1)/(4)*\text{ Slope of perpendicular line = -1} \\ \text{Slope of perpendicular line = -1}*(-(4)/(1)) \\ \text{Slope of perpendicular line =}4 \end{gathered}`

Hence,

Slope of parallel line: -(1/4),

Slope of perpendicular line: 4.