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=-(1)/(m_1)`

We have

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

Therefore

`m_2=-(1)/(-2)=(1)/(2)`

We have the equation of a line:

`y=(1)/(2)x+b`

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

`4=(1)/(2)(-2)+b`

`4=-1+b` add 1 to both sides

`5=b\to b=5`

Answer:
`\boxed{y=(1)/(2)x+5}`