Question

What is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ?

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=-(4)/(5)x+3\to m_1=-(4)/(5)`

Therefore

`m_2=-(1)/(-(4)/(5))=(5)/(4)`

We have the equation of a line:

`y=(5)/(4)x+b`

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

`12=(5)/(4)(4)+b`

`12=5+b` subtract 5 from both sides

`7=b\to b=7`

Answer:
`\boxed{y=(5)/(4)x+7}`