Question

What is an equation of the line that is perpendicular to y=−45x+3 and passes through the point (4, 12) ?

Answer 1

y=5/4x + 7

Explanation:

Answer 2

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=-45x+3\to m_1=-45`

Therefore

`m_2=-(1)/(-45)=(1)/(45)`

We have the equation of a line:

`y=(1)/(45)x+b`

Put the coordinates of the point (4, 12) to the equation of a line:

`12=(1)/(45)(4)+b`

`12=(4)/(45)+b` subtract
`(4)/(45)` from both sides

`11(41)/(45)=b`

Answer:
`\boxed{y=(1)/(45)x+11(41)/(45)}`