# How do you find the slope perpendicular to 2x + 3 = 4y?

Jan 20, 2016

Perpendicular slope has value $- 2$

#### Explanation:

Since the given equation is a simple linear equation, it's not difficult to find the slope perpendicular to the given equation.
Now, we know that the product of the value of the slopes of 2 perpendicular lines is equal to negative of unity, that is
${m}_{1} \cdot {m}_{2} = - 1$
The above equation should first be made into a general slope equation first, so it becomes
$2 \left(x + \frac{3}{2}\right) = 4 y \setminus \implies y = \frac{1}{2} \left(x + \frac{3}{2}\right)$
So the slope of the above given equation is taken as ${m}_{1} = \frac{1}{2}$
Now, substituting this in the given equation, we get ${m}_{2} \cdot \frac{1}{2} = - 1 \setminus \implies {m}_{2} = - 2$