Question

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5 ?

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=-(2)/(3)x+5\to _1=-(2)/(3)`

Therefore

`m_2=-(1)/(-(2)/(3))=(3)/(2)`

We have the equation of a line:
`y=(3)/(2)x+b`.

Put the coordinates of the point (8, 1) to the equation of a line:

`1=(3)/(2)(8)+b`

`1=(3)(4)+b`

`1=12+b` subtract 11 from both sides

`-11=b\to b=-11`

Answer:
`\boxed{y=(3)/(2)x-11}`