# What is the slope of the line perpendicular to  y=-2 x+3 ?

Apr 10, 2016

The perpendicular slope is: $\frac{1}{2}$

#### Explanation:

The slope of a line perpendicular to a liner function is described as the negative reciprocal.

This basically means that to find the slope of the line perpendicular to any linear function, we flip the slope of the equation we are given upside down and multiply that number by $- 1$.

If we consider your equation:

$y = - 2 x + 3$ we can see that the slope of the line is $- 2$ (the coefficient of the $x$ term.

Recall that we can write a whole number as a fraction by using a denominator of 1 i.e. $3 = \frac{3}{1}$

In your case we can write $- 2$ as $- \frac{2}{1}$.

Remember that calculating the reciprocal of a number is flipping it upside down?

We can write the reciprocal of $- \frac{2}{1}$ as $- \frac{1}{2}$.

In our final step to calculate a perpendicular linear slope we multiply the reciprocal by $- 1$

$- \frac{1}{2} \cdot - 1 = \frac{1}{2}$
Therefore, we can now state that the slope of the line perpendicular to the function $y = - 2 x + 3$ is: $\frac{1}{2}$