# What is an equation of the line that has a y-intercept of -2 and is perpendicular to the line x-2y = 5?

Nov 19, 2015

$2 x + y = - 2$

#### Explanation:

Write as ${y}_{1} = \frac{1}{2} x - \frac{5}{2}$

If you have standard form of $y = m x + c$ then the gradient of its normal is $- \frac{1}{m}$

The gradient of a line normal to this is $- 1 \times {\left(\frac{1}{2}\right)}^{\text{inverted}} = - 2$

As it passes through y=02 at x=0 then the equation becomes:

${y}_{2} = - 2 x - 2$

In same form as question gives:

$2 x + y = - 2$