Question

Write an equation of a line perpendicular to y=4x-3 that contains the point (0,7)

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=4x-3\to m_1=4`

Therefore

`m_2=-(1)/(4)`

We have the equation of a line:

`y=-(1)/(4)x+b`

Put the coordinates of the point (0, 7) to the equation of a line:

`7=-(1)/(4)(0)+b\\\\\7=b\to b=7`

Answer:
`\boxed{y=-(1)/(4)x+7}`