Question

What is an equation of the line perpendicular to y=-2x-2 and through (-2,4)

Answer 1

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have

$y=-2x-2\to m_1=-2$

Therefore

$m_2=-\dfrac{1}{-2}=\dfrac{1}{2}$

We have the equation of a line:

$y=\dfrac{1}{2}x+b$

Put the coordinates of the point (-2, 4) to the equation of a line:

$4=\dfrac{1}{2}(-2)+b$

$4=-1+b$      add 1 to both sides

$5=b\to b=5$

Answer: $\boxed{y=\dfrac{1}{2}x+5}$