# How do you find the slope perpendicular to y=2x-3?

Apr 14, 2018

$- \frac{1}{2}$

#### Explanation:

the product of the slope of the normal and the slope of the line

must be = -1 is they are perpendicular to one another

the line $y$ = 2$x$ - 3 is in the form $y$ = m$x$ + b

where m is the slope so the slope for this line is 2

then Slope of Normal $\cdot$ 2 = -1

slope of normal = $- \frac{1}{2}$

Apr 14, 2018

$- \frac{1}{2}$

#### Explanation:

Perpendicular slopes are opposite reciprocals of one another. In the equation, the slope is $2$ (it's in the form $y = m x + b$, where $m$ is the slope).

Opposites (negative version of a positive number and vice versa):

$- 3 , 3$

$\frac{2}{4} , - \frac{2}{4}$

$\frac{13}{9} , - \frac{13}{9}$

Reciprocals (switch the numerator and denominator):

$\frac{1}{2} , 2$

$\frac{13}{7} , \frac{7}{13}$

$- 23 , - \frac{1}{23}$

The opposite number of $2$ is $- 2$ and the reciprocal of $- 2$ is $\frac{1}{2}$.