# How do you find the slope of the line perpendicular to 4x+2y=10?

Apr 4, 2015
• The Product of the Slopes of 2 Perpendicular Lines is always $- 1$

• So let's find the Slope of the given line first

The equation of the line is $4 x + 2 y = 10$

The Slope Intercept form of the equation of a given line is $y = m x + c$ where $m$ is its slope, and $c$ is its Y intercept.

To get the slope intercept form of the given line, we transpose $4 x$ to the other side. We get

$2 y = - 4 x + 10$

Dividing both sides of the equation by 2, we get:

$y = - 2 x + 5$

The Slope of the given line is $- 2$. Let's call it ${m}_{1}$. And let the slope of the line Perpendicular to this line be called ${m}_{2}$

• As the Product of the Slopes of 2 Perpendicular Lines is $- 1$, we can say that
${m}_{1} \cdot {m}_{2} = - 1$
$\left(- 2\right) \cdot {m}_{2} = - 1$
${m}_{2} = \frac{1}{2}$

• The Slope of the line Perpendicular to $4 x + 2 y = 10$ is $\frac{1}{2}$