# How do you find an equation of a line containing the point (-2, 2), and perpendicular to the line 2(y + 1) = x?

Sep 6, 2017

See explanation.

#### Explanation:

First we have to transform the given equation to form $y = a x + b$ :

$2 \left(y + 1\right) = x$

$2 y + 2 = x$

$2 y = x - 2$

$y = \frac{1}{2} x - 1$

Now we can write the equation of a line perpendicular to the given one.

Two lines are perpendicular if and only if product of their slopes is $- 1$:

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

$m = - 2$

So the line we are looking for has equation:

$y = - 2 x + b$

Now we have to calculate the value of $b$ for which point (-2;2) belongs to the line:

To do this we have to put the point's coordinates as $x$ and $y$:

$2 = - 2 \cdot \left(- 2\right) + b$

$2 = 4 + b$

$b = - 2$

Finally the line perpendicular to $2 \left(y + 1\right) = x$ passing rhrough $\left(- 2 , 2\right)$ is