Question

What is an equation of the line perpendicular to y=-x-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=-x-2\to m_1=-1`

Therefore

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

We have the equation of a line:

`y=-1x+b\to y=-x+b`

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

`4=-(-2)+b`

`4=2+b` subtract 2 from both sides

`2=b\to b=2`

Answer: y = -x + 2