# How do you find the slope that is perpendicular to the line 4x-8y=-1?

Jul 21, 2016

Slope is $- 2$

#### Explanation:

Recall that we can perform operations on an equation as long as we do the same thing to both sides.

Add $8 y$ to both sides:

$4 x = 8 y - 1$

Add $1$ to both sides:

$4 x + 1 = 8 y$

Divide both sides by 8:

$y = \frac{1}{2} x + \frac{1}{8}$

This is now in standard form $y = m x + c$ so we can read off that the slope of our original line is $\frac{1}{2}$.

Now, an important and useful fact is that the product of two perpendicular gradients is always equal to $- 1$. This means that if we know a slope, we can work out a slope that will be perpendicular to it.

${m}_{1} {m}_{2} = - 1$

${m}_{2} = - \frac{1}{m} _ 1$

${m}_{1} = \frac{1}{2} \implies {m}_{2} = - 2$