if $y = mx + b$ is the equation of a line perpendicular to the line $y = 5x - 2$, what is the value of…

if $y = mx + b$ is the equation of a line perpendicular to the line $y = 5x - 2$, what is the value of $m$?\n$m=-\frac{1}{5}$\n$m=\frac{1}{5}$\n$m = 5$\n$m = -5$

if $y = mx + b$ is the equation of a line perpendicular to the line $y = 5x - 2$, what is the value of $m$?\n$m=-\frac{1}{5}$\n$m=\frac{1}{5}$\n$m = 5$\n$m = -5$

Answer

Explanation:

Step1: Identify given slope

The slope of $y=5x-2$ is $m_1=5$.

Step2: Apply perpendicular slope rule

Perpendicular slopes multiply to -1: $m \times m_1 = -1$ $\implies m = \frac{-1}{m_1}$ $\implies m = \frac{-1}{5}$

Answer:

$m=-\frac{1}{5}$ (first option)