Given:
The given equation of a line is,
[tex]y=-\frac{1}{4}x+2[/tex]
The objective is to find the slope of a parallel line and the slope of a perpendicular line.
Explanation:
The general equation of a straight line is,
[tex]y=mx+b[/tex]
Here, m represents the slope of the equation.
By comparing the general equation with the given equation,
[tex]m=-\frac{1}{4}[/tex]
To find slope of parallel lines:
The slope value of two parallel lines will always be equal.
[tex]\text{Slope of parallel line =-}\frac{1}{4}[/tex]
To find slope of perpendicular line:
But for perpendicular lines the product of slope value of two perpendicular lines will be (-1).
[tex]\begin{gathered} m\times\text{Slope of perpendicular line = -1} \\ -\frac{1}{4}\times\text{ Slope of perpendicular line = -1} \\ \text{Slope of perpendicular line = -1}\times(-\frac{4}{1}) \\ \text{Slope of perpendicular line =}4 \end{gathered}[/tex]
Hence,
Slope of parallel line: -(1/4),
Slope of perpendicular line: 4.
