# How do you find the slope of a line perpendicular to y = 2 - 5x?

May 1, 2018

To find perpendicular gradient, $m 1 \cdot m 2 = - 1$

#### Explanation:

Remember that the slope of the line is known as gradient, and is often represented as $m$

First rearrange the function into the gradient-intercept form $y = m x + c$:

$y = 5 x - 2$

Here we can see that the gradient of the function is 5, because $m = 5$

Next use $m 1 \cdot m 2 = - 1$ , to find the perpendicular gradient.

$5 \cdot m 2 = - 1$
$\frac{5 \cdot m 2}{5} = - \frac{1}{5}$
$m 2 = - \frac{1}{5}$, or -0.2.

The perpendicular gradient is -0.2

May 1, 2018

Slope of a line perpendicular to $y = - 5 x + 2$ is $\frac{1}{5}$

#### Explanation:

Slope of the line,  y= -5 x +2 ; [y=m x+c]

is ${m}_{1} = - 5$ .The product of slopes of the perpendicular lines is

${m}_{1} \cdot {m}_{2} = - 1 \therefore {m}_{2} = \frac{- 1}{m} _ 1 = \frac{- 1}{-} 5 = \frac{1}{5}$. Therefore, slope of

a line perpendicular to $y = - 5 x + 2$ is $\frac{1}{5}$ [Ans]